Pore Pressure Estimation From Velocity Data: Accounting for Overpressure Mechanisms Besides Undercompaction Glenn L.. As a result, the sonic velocity will not go down the virgin curve
Trang 1Pore Pressure Estimation From Velocity Data: Accounting for Overpressure
Mechanisms Besides Undercompaction
Glenn L Bowers,” Exxon Production Research Co
Summary
A new method for estimating pore pressure from formation sonic ve-
locity data is presented Unlike previous techniques, this method ac-
counts for excess pressure generated by both undercompaction, and
fluid expansion mechanisms such as aquathermal pressuring, hydro-
carbon maturation, clay diagenesis, and charging from other zones
The method is an effective stress approach; the effective stress is
computed from the velocity, and the result is subtracted from the over-
burden stress to obtain pore pressure To include multiple sources of
overpressure, a pair of velocity-vs.-effective-stress relations are
introduced One relation accounts for normal pressure and overpres-
sure caused by undercompaction The second is applied inside veloc-
ity reversal zones caused by fluid expansion mechanisms
Example applications of the method are presented from the U.S
gulf coast, the Gulf of Mexico, and the Central North Sea Some oth-
er pore pressure estimation approaches are also examined to demon-
strate how these techniques have unknowingly accounted for over-
pressure mechanisms other than undercompaction
It is also explained how velocity-vs.-effective-stress data can be
used to identify the general cause of overpressure in an area For
instance, the empirical correlation of Hottman and Johnson indi-
cates that overpressure along the U.S gulf coast cannot be due only
to undercompaction
Introduction
Numerous methods have been developed for estimating pore fluid
pressure from geophysical data, and the list continues to grow Empir-
ical approaches equate departures from the normal trend line of some
porosity-dependent measurement to an equivalent pore pressure gra-
dient Recent methods have followed the more fundamental effective
stress approach pioneered by Foster and Whalen,! Ham,’ and Eaton.3
All current pore pressure estimation methods fail to formally take
into account the cause of overpressure It will be demonstrated that
this can lead to significant errors For a given velocity at a given
depth, the pore pressure can vary by 4 !bm/gal or more, depending
upon how the excess pressure was generated
This paper presents a method for estimating pore pressure from
sonic velocity data that systematically accounts for the cause of
pressure When applied to wireline sonic logs, it is preferable to only
use shale data to minimize the effects of lithology changes Howev-
er, the method is also applicable for pre-drill predictions from seis-
mic interval velocities
The paper begins with a review of fundamental aspects of shale com-
paction behavior that form the foundation of this method This is fol-
lowed by a discussion of how different causes of overpressure affect
the sonic velocity Some current pore pressure estimation methods are
then examined in light of these concepts The new method is then de-
scribed, and example applications are presented and discussed
Compaction Behavior
Non-Decreasing Effective Stress States, Under increasing effec-
tive pressure, sediments compact, and their sonic velocity goes up
At the limit, their porosity approaches zero, and their sonic velocity
approaches the value for the sediment grains Borrowing terminolo-
*Now with Applied Mechanics Technologies
Copyright 1995 Society of Petroleum Engineers
Original SPE manuscript received for review March 10, 1994 Revised manuscript received
Nov 30, 1994 Paper accepted for publication Feb 27, 1995 Paper (SPE 27488) first pres-
ented at the 1994 IADC/SPE Drilling Conference heid in Dallas Feb 15-18
SPE Drilling & Completion, June 1995
gy from soil mechanics, the velocity-effective stress relation for non-decreasing effective stress states will be referred to as the virgin curve Fig 1a plots shale virgin curve data derived from well log and RFT measurements from the Gulf of Mexico slope, and shows
an estimate of the complete virgin curve
Effective Stress Reductions Much (but not all) of the porosity loss/ velocity gain that occurs during compaction is permanent As a result, the sonic velocity will not go down the virgin curve when the effective stress is reduced (unloading) The velocity will track a different, fast-
er velocity-vs.-effective-stress relation that will be called the unload- ing curve If the effective stress is subsequently increased, the veloc- ity will follow the unloading curve back to the virgin curve Fig 1b illustrates unloading behavior with laboratory velocity- effective stress data for Cotton Valley shale (Tosaya*), The veloci- ties measured at effective stresses below the maximum in-situ stress state must be on an unloading curve For-cémparison, the virgin curve for the Gulf of Mexico sediments is replotted in Fig Ib Overpressure Causes/Effects
Normal Pressure During burial under normal pressure conditions, the effective stress continually increases with depth Consequently, normal trend velocity-vs.-effective-stress data follow a virgin curve Undercompaction Overpressure most commonly occurs when pore fluid trapped by low permeability is squeezed by the weight of newly deposited sediments This overpressuring process is referred
to as undercompaction or compaction disequilibrium
Undercompaction cannot cause the effective stress to decrease Therefore, the virgin curve also applies for formations overpres- sured by undercompaction The most undercompaction can do is
“freeze” the effective stress in time, which would cause the velocity
to become fixed on the virgin curve On a velocity/depth plot, this would appear as a velocity plateau
Fig 2 illustrates undercompaction overpressure in the Gulf of Mexico Pore pressure, sonic velocity, and stress information are shown in Figs 2a, 2b, and 2c, respectively Fig 2d plots velocity- vs.-effective- stress data determined at RFT locations It can be seen that all of data in Fig 2d appear to lie on a virgin curve, and that the points below 7200 ft are approaching a fixed point
Fluid Expansion Overpressure can also be generated by fluid ex- pansion mechanisms such as heating,>-© hydrocarbon maturation,” charging from other zones,® and expulsion/expansion of intergranu- lar water during clay diagenesis.! Here, excess pressure results from the rock matrix constraining the pore fluid as the fluid tries to increase in volume
Unlike undercompaction, fluid expansion can cause the pore pressure to increase at a faster rate than the overburden stress This forces the effective stress to decrease as burial continues, which pro- duces a velocity reversal (see Fig 3b) Velocities inside the reversal will track an unloading curve(s), while velocities outside the rever- sal will remain on a virgin curve
Fig 3 illustrates this with data from an Indonesian well Pore pressure, velocity, and stress data are displayed in Fig 3a, 3b, and 3c, respectively, while Fig 3d compares velocity-vs-effective- stress data from inside (open circles) and outside (solid circles) the velocity reversal The start of the reversal coincides with the top of overpressure at approximately 6350 ft
It can be seen in Fig 3d that the velocities from inside the reversal track a much faster trend This suggests that fluid expansion mecha-
89
Trang 2Depth
90
17
157
L
137
s
=
9 -
7 ® Gulfí of Mexico
In Situ Data
5 L L al i L L
0 2 4 6 8 10 12 14 16 18
Effective Stress (ksi)
a)
F Unloading Curve
15Ƒ \ 8 8 92
°
13 fF
ze -
=
3 Mexico Data
© Tosaya (1982) Cotton
Valley Shale Lab Data
4 L 1 i 1 1 i
0 2 4 6 8 10 12 14
-_Effective Stress (ksi)
b) Fig 1—Shale compaction behavior: (a) virgin curve and (b) unloading curve
16 18
Pore Pressure (ppg) Velocity (ktt/s) Stress (ksi) Effective Stress (ksi)
8 10 12 14 16 18 20 § 75 10 125 15 0 2 4 6 8 10 0 1 2 3 4
a @ RFT's
11
er
F Pore
Pressure
=
5 8£
aL
©
Fig 2^—Undercompaction overpressure—Gulf of Mexico
B 10 12 14 16 18 20 § 7 9 11 13 15 17 09 2 4 6 8 10 0 1 2 3
6543' -
Stress |a0ag;.“ 57a9'
10 fo -” 9 6950'
Reversal Pore _v\ 7T
` Virgn ® Outside
ag Cure Reversal
10
Fig 3—-Fluid expansion overpressure offshore indonesia
SPE Drilling & Completion, June 1995
Trang 3
12
11
10
a
s9
>
8
3 8
>
7
Pore Pressure
@ 9-15 ppg
0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7
Effective Stress (ksi) Effective Stress (ksi)
Fig 4—Fiuid expansion overpressure, Gulf of Mexico
nisms contributed to the overpressure inside the reversal Note the
similarity between the unloading curve in Fig 3d and the trend fol-
lowed by the Cotton Valley shale data in Fig 1b
Fig 3d also demonstrates the importance of accounting for the
cause of overpressure when estimating pore pressures The virgin
curve would overestimate the effective stress at 6950 ft by 1700 psi,
which means the pore pressure would be underestimared by the
same amount This would correspond to a 4.7 lbm/gal! error in the
equivalent mudweight prediction
Fig 4 present further evidence of unloading Fig 4a shows veloc-
ity-effective stress data derived from RFT and well log measure-
ments along the Gulf of Mexico slope The data are divided into two
groups according to the magnitude of overpressure Solid circles are
in the 9 to 15 Ibm/gal equivalent mudweight range, while the open
circles are in “hard” overpressure Contrary to what might be ex-
pected, the higher pressure data tend to have faster velocities As
Fig 4b indicates, a possible explanation is that most of these data
are from formations that have undergone some unloading Similar
trends are evident in the Central North Sea velocity-vs.-effective-
stress data plotted in Fig §
Others have also reported evidence of unloading caused by high
pressure Magara!! found that the Equivalent Depth method under-
predicted the pore pressure data of Hottman and Johnson.!2 The
equivalent depth method? equates the effective stress in an over-
pressured zone to that in a normally pressure interval with the same
velocity (see Fig 6) This assumes that the overpressure data are on
a virgin curve If fluid expansion has driven the data onto an unload-
ing curve, as in Fig 3, the effective stress will be overestimated, and
the pore pressure will be underestimated, as Magara observed
0
` Effective Stress
i `
\ \
I `
Estimated
SF Sonic \ Pore Pressure at 7200 ft
Log Normal Actual (RFT) = 15.9 ppg
10 ‘ mm pe
Velocity (ktV/s) Stress (ksi)
Fig 6—Case where equivalent depth method works—Gulf of
Mexico
SPE Drilling & Completion, June 1995
15
Unloading
ƑỊ Curve for 46 Each Vmax #5
3
i, ‘
Pore Pressure
?7† Virgin @ 8-13 ppg
Curve © 14-18 ppg
5 L 1 1 L 1 L L_
Effective Stress (ksi) Fig 5—Fluid expansion overpressure, central North Sea Plumley!? discussed unloading caused by fluid expansion over- pressure, and presented a U.S gulf coast example of its occurrence
He compared porosities from an overpressured and normally pres- sured interval having the same effective stresses The porosity in the overpressured zone was half the value in normal pressure (17.6% vs 38%) Piumley concluded this was because the high pressure zone had undergone unloading Berg and Habeck!4 came up with a simi- lar conclusion using density log data from a south Texas well Velocity Reversal Without Unloading Not all velocity reversals are caused by fluid expansion mechanisms The velocity will also drop across the transition from a normally pressured sand/shale se- quence to a massive undercompacted shale If fluid expansion is not the cause, the velocity-vs.-effective-stress data from the reversal will follow a virgin curve
Determining the Cause of Overpressure In Velocity Reversals
A reliable way has not been found to determine from velocity data alone whether a reversal was caused by undercompaction or fluid expansion However, some general guidelines can be offered on the geologic conditions that are conducive to each of these causes of pressure (Miller and Luk®)
The amount of overpressure generated by undercompaction de- pends upon the relative compressibility of the rock matrix and the pore fluid They act like two springs in parallel If the rock matrix
is much more compressible, increases in overburden stress will be carried primarily by the pore fluid If the rock matrix is much less compressible, then it will bear most of the overburden Therefore, undercompaction will typically generate the greatest overpressure
at shallower depths, where formations are soft
0
r Overburden Svess
2 F \ Effective Stress
[ Normal Pore
Pressure _ 4
8 + Pore Pressure at 6950 tt
Actual (RFT) = 16.2 ppg Estimated = 11.7 ppg
10 + oh 4 va 4s i
5 75 10 12.5 0 2 4 6 8 10
Velocity (ktt/s) Stress (ksi) Fig 7—-Case where equivalent depth method fails—offshore In- donesia
91
Trang 4
Velocity (kf/4) Pore Pressure (ppg) Effective Stress (ksi)
| + Assumed © Pressure Tests Vmax ⁄
14Ƒ $ ` F f Normal @ Outside Reversal
Trend {Normal Trend}
Fig 8—U.S gulf coast application of the Hottman & Johnson and equivaient depth methods
On the other hand, the activity of many fluid expansion mecha-
hisms increases with temperature, and therefore depth To be a
strong source of overpressure, fluid expansion also requires a fairly
rigid, well-compacted rock matrix that can adequately constrain the
pore fluid Consequently, fluid expansion is more likely to be an im-
portant source of overpressure at deeper depths, in stiffer rocks
The only sure way to determine the cause of overpressure in a ve-
locity reversal is with measured pore pressures One way is to plot
velocity-vs.-effective-stress data from inside and outside the rever-
sal, as in Fig 3d The reversal data will track a much faster trend if
fluid expansion mechanisms were active
Another approach is to compare measured pore pressures with
those computed with the equivalent depth method The equivalent
depth method will underestimate pore pressure caused by fluid ex-
pansion Figs 6 and 7 present cases where the equivalent depth
method works and fails
Cementation Unloading may not be the only reason that velocity
reversal data deviate from the virgin curve; cementation could also
be a factor From the standpoint of pore pressure estimation, this is
inconsequential What counts is that the separate trend tracked by
the reversal data be recognized and accounted for
However, cementation does complicate diagnosing the cause of
overpressure within a reversal Even with petrographic analyses, it
can be difficult to sort out the relative effects of unloading and ce-
mentation What can be said is that cementation is conducive to fluid
expansion overpressure, because it increases the rock matrix’s
constraint of the pore fluid Consequently, while local geologic
conditions must be considered, there is reason to believe that under-
compaction is generally not the sole source of overpressure when
velocity reversal data diverge significantly from the virgin curve
Velocity (ktt/s) Pore Pressure (ppg)
§ 7.5 10 12.5 15 8 10 12 14 16 18
0 Y T Y T +“ T Y T
Trend
_ 6 [ [
z
ier \ [ Equivalent Ỏ
Current Pore Pressure Estimation Methods Most pore pressure estimation methods claim to only be applicable for overpressure caused by undercompaction However, it turns out that many current pore pressure estimation methods are (unknow- ingly) predicting fluid expansion overpressure To illustrate this, two popular techniques are examined
Hottman and Johnson The Hottman and Johnson (H&J) method empirically correlates departures from the velocity normal trend line to an equivalent pore pressure gradient.!2 Empirical correla- tions have no inherent bias towards one particular overpressure mechanism They simply reflect whatever the dominant cause of overpressure is in the area in which they were developed For their U.S gulf coast correlation, H&J assumed this was undercompac- tion If this is true, then the Equivalent Depth and H&J methods should give similar results As a test, both approaches were applied
to shale sonic log data from H&J’s original paper!? (Well “R”) Fig 8a shows the velocities, while Fig 8b compares the estimated pore pressures with bottomhole pressure measurements
It can be seen that the equivalent depth method underpredicts the pressure, while the H&J correlation performs well This has two pos- sible implications First, because the Equivalent Depth method failed, this suggests that fluid expansion is an important source of overpres- sure Second, because the H&J method worked, H&J’s Gulf Coast correlation appears to have fluid expansion “built” into it
As further evidence, Fig 8¢ plots velocity-vs.-effective-stress data from the well Solid circles are from the normal trend line Ea- ton’s U.S gulf coast overburden stress curve!5 and a normal pres- sure gradient of 0.465 psi/ft were used to estimate effective stresses
at these points Open circles are from the three pressure tests inside
Effective Stress (ksi)
0 i 2 3 4 5 6
Reversa! T= Pnorm( Vv )
©
>8Ƒ sf ye
6 / (Pressure Tests) C= Cnorm( 7 )
c) Fig 9—U.S gulf coast application of the Eaton and equivalent depth methods
92 SPE Drilling & Completion, June 1995
Trang 5the velocity reversal The faster trend tracked by the reversal data
1s characteristic of unloading
The solid line in Fig 8c is the velocity-vs.-effective-stress path
defined by H&J’s pore pressure estimates inside the reversal This
curve clearly deviates from the normal pressure data, which again
suggests the H&J Gulf Coast correlation is biased towards fluid ex-
pansion overpressure This also means that this correlation will
overestimate the pore pressure at wells where undercompaction tru-
ly is the dominant cause of overpressure, as in Fig 2
Eaton Original Eaton Method Eaton’s method? is an effective stress
approach, with the effective stress, 0, computed from the equation:
3
O= nom (7)
Here v is the measured velocity, and Oporm and Vnorm are the values
the effective stress and velocity should have under normal pressure
conditions Eq 1 implies that normally pressured and overpressured
formations both follow a virgin curve relation of the form:
Consequently, Eaton’s method should underestimate fluid expan-
sion overpressure
The velocity normal trend line is usually assumed to be a straight
line on a plot of log(Vporm) vs depth However, according to Eq I,
V and Vnorm Should both satisfy Eq 2 Therefore, to be consistent,
Vnorm Should actually be calculated from Eq 2 using Onorm values
determined from the overburden stress and normal pore pressure
profiles If this were done, the normal trend line would not be a semi-
log straight line
Fig 9a compares H&J’s semi-log normal trend for Well R (dot-
dashed curve) with one analytically computed from Eq 2 (solid
line) The parameter C = 564 was obtained by fitting Eq 2 through
the normal trend velocity-effective stress data in Fig 9c It can be
seen that the semi-log normal trend line is faster than the analytical
solution below the top of overpressure By overestimating Vporm, the
semi-log normal trend will make Eq 1 predict lower effective
Stresses, and therefore higher pore pressures than Eq 2 This will
generally be true However, unless unreasonably large values are as-
sumed for Vporm, Eq 1 will still underestimate fluid expansion over-
pressure
This is the case with the Eaton pore pressure estimates for Well
R, which are plotted as a solid line in Fig 9b The dot-dashed line
is the equivalent depth solution It can be seen that both methods fall
well short of the measured pressures in the velocity reversal The ve-
locity-effective stress data in Fig 9c explain why Even with the
semi-log normal trend line, the Eaton solution inside the reversal re-
mains close to the virgin curve defined by Eq 2
Perfectly Plastic
(Us 00)
Typical
Unloading Curve
(U = 3 to 8)
Z
g
Vinax max
.Z
Perfectly
Elastic
(U=1.0)
⁄
Virgin Curve:
V=s5000+A 0 Unloading Curve:
V=5000+A [m»«.(0/z.)
Virgin
Effective Stress
Fig 10—The unloading parameter “U.”
SPE Drilling & Completion, June 1995
Modified Eaton Method If the Eaton pore pressure estimates are too low, Eq | can be adjusted to yield lower effective stresses One way is to increase Vaorm by shifting and rotating the normal trend line (Weakley!®) Another, simpler alternative, is to raise the exponent in
Eq 1 Either way, the net effect is the same: it allows the original Ea- ton virgin curve relation to be transformed into an unloading curve
For example, by raising the exponent from 3 to 5, the revised Ea-
ton solution (dotted line in Fig 9b) is able to closely match the Well
R pressure data As Fig 9c shows, this is because the higher expo- nent has allowed Eaton’s equation to simulate an unloading curve New Method
Overview The new method is an effective stress approach that em-
ploys virgin and unloading curve relations to account for both un- dercompaction and fluid expansion overpressure Effective stresses outside of velocity reversal zones are computed from the virgin curve Inside a velocity reversal, offset well data are used to decide which equation is appropriate For rank wildcats, the pore pressure can be computed both ways to establish lower and upper bounds on the pressure The unloading curve will always yield higher pore pressure estimates
Virgin Curve Over stress ranges of practical interest, it has been
found that the virgin curve for shale, as shown in Fig 1a, can be ade- quately represented by the following equation:
where v is velocity (ft/s), 0 is effective stress (psi), and A and B are parameters calibrated with offset velocity-vs-effective-stress data Unloading Curve The unloading curve is defined by the empirical relation:
v=5000 + A[0max (0/Ømax)(/UJIB (4
where A and B are as before, U is a third parameter, and
5000\ /"
Vmax~
Here, Omax and Vmax are estimates of the effective stress and velocity
at the onset of unloading
In the absence of major lithology changes, Vmax is usually set equal to the velocity at the start of the velocity reversal This as- sumes that all formations within the reversal at one time passed through the same maximum stress state While this generally may not be true, using the velocity at the start of the reversal for Vmax has been found to work satisfactorily
1
Qo
0.8 F Normalized
® * Unloading Curve
#P (max) > (-\nsax)
— 06E
g Unloading
% Wella 5
® Weil #3 0.2 Well #4 ‘ :
O Weias oc T, Tron
0 L 4 L L
0 0.2 0.4 0.6 0.8 1
(0a) Fig 11—Normalized unloading curve
93
Trang 6
ot r © Pressure Tesis Vmax
= 6} Ss eo F s , J a oe Œ °
‘ore
3° ° [ Pressure Ber ¿
a 10F a Vmax L g > ; °
Fig 12—U.S gulf coast application of new method
The unloading parameter U is a measure of how plastic the sedi-
ment is (see Fig 10) U = 1 implies no permanent deformation, be-
cause the unloading curve reduces to the virgin curve U = © corre-
sponds to completely irreversible deformation, since v = Vmax for all
values of effective stress less than Omax In practice, U typically
ranges between 3 and 8
Solving for U While virgin curve data track a single curve, unload-
ing data from multiple wells will generally lie on multipte unloading
curves (see Fig 5) However, by substituting Eq 3 into Eq 4, the
unloading curve can be recast into a form that normalizes multiple
well unloading data onto a single curve:
where
1/B
Oye = (=#) ¬—— b eee teteeteneeneenes (7)
As the insert in Fig 11 illustrates, o,, is the stress at which the cur-
rent velocity v intersects the virgin curve Fig 11 shows the normal-
ized version of the unloading data in Fig 5
Example Applications
U.S Gulf Coast Fig 12 shows an application of the new method
to Hottman and Johnson’s Well R The virgin curve parameters
(A = 4.4567, B =0.8168) were determined by fitting velocity-vs.-
effective-stress data from the normal pressure interval above 10000
ft (see Fig 12c) A normal pressure gradient of 0.465 psi/ft, and Ea-
ton’s U.S gulf coast overburden stress curve were used to estimate
effective stresses along the normal trend The normal trend line in
Fig 12a was calculated from the virgin curve relation
Velocity (ktt/s)
Ệ 6 7 8 9 10 11 8 10 T 42 T 14 T— 16 18
Pore Pressure (ppg)
` ORFTS
Fig 13~-Deepwater Gulf of Mexico example
94
Pore pressures inside the velocity reversal were computed from the unloading curve relation, with U =3.13 This is a regional un- loading parameter determined from U.S gulf coast and Gulf of Mexico data Fig 12b compares the pressure estimates with the measured values The accuracy achieved is similar to that for the Hottman & Johnson U.S gulf coast correlation
Fig 12c compares the virgin curve and unloading curve relations with velocity-effective stress data from inside and outside the rever- sal Also shown is the velocity-vs.-effective-stress path defined by H&J’s pore pressure estimates inside the reversal As can be seen, the new method’s unloading curve is very close to H&J’s stress path Their divergence is due to the Hottman and Johnson normal trend line exponentially increasing with depth
Deepwater Gulf of Mexico The next example is from a well drilled
in nearly 1400 ft of water in the Gulf of Mexico Fig 13a plots the sonic log data, and a norma! trend line analytically computed from
Eq 3 There are a number of smail velocity reversals above 9700 ft, and one major reversal between 9700 ft and TD Because all of the shallower reversals are very weak, they were not considered to be due to fluid expansion
Within the large reversal, the velocity at first drops at arate similar
to that in the smaller reversals However, at 10200 ft, the slope steep- ens significantly This slope break was interpreted to be the onset of fluid expansion overpressure Therefore, in the unloading relation, Vmax Was assumed to be the velocity at 10200 ft, not the peak veloc- ity at 9700 ft Where the velocities near TD are above the value at
10200 ft, the virgin curve was used to compute effective stresses
As in the U.S gulf coast example, a value of 3.13 was assumed for the unloading parameter U Regional virgin curve parameters, determined from wells in water depths between 600 and 1500 ft were used for A and B, with A = 28.3711, B=0.6207
Velocity (kit/s) Pore Pressure (ppg)
§ 7.5 10 125 15 175 20 8 10 12 14 #16 18 20
0 + + + + + Y T T T T
~~
' Used
Method
ee ==" —-—.—-:—- ain a
X-Unconlormity
Fig 14—Central North Sea example
SPE Drilling & Completion, June 1995
Trang 7Fig 13b plots the pore pressure data Open circles are pore pres-
sures determined from RFT measurements The dotted line shows
the mudweights that were used, while the solid line is the estimated
pore pressure It can be seen that the new method is able to track both
the rise in pressure, and the pressure regression
Central North Sea The final example is from a high pressure/high
temperature (HPHT) well in the Central North Sea Fig 14a shows
the sonic log data, and three separate normal trends; one for the Ter-
tiary shales above 9000 ft (A = 2.8746, B =0.9037), another for the
chalk (A = 802.1, B= 0.3215), and a third for all other formations
above and below the chalk (A = 8.116, B = 0.8002)
Overpressure above the chalk is primarily due to undercompac-
tion, while below the chalk, fluid expansion mechanisms appear to
be important This is evident from the velocity-effective stress data
in Fig 5 The 8 to 13 Ibm/gal group (solid circles) includes forma-
tions from above and below the chalk All of the data in the 14 to 18
lbm/gal range (open circles) are from Jurassic formations below the
X-unconformity A fit of the normalized Central North Sea unload-
ing data in Fig 11 yielded U = 4.48
There are essentially no normally pressured shale intervals along this
well Consequently, it would be very difficult to apply pore pressure es-
timation methods that rely on a normal trend line This would include
empirical correlations, the equivalent depth, and Eaton methods
Near the top and bottom of the chalk, velocity changes due to pore
pressure are obscured by those due to lithology Significant variations
in sonic properties also occur within the chalk Consequently, pore
pressure estimates in and near the chalk are not considered reliable
To compensate for lithology effects, the following approach was
used Above the chalk, pore pressures estimated down to the onset
of the rapid velocity rise at 9800 ft were honored Pore pressures
computed below the X-unconformity were also assumed to be valid
The estimates on either side of the chalk were then connected with
straight lines to the pore pressure calculated at the first major veloc-
ity peak within the chalk
Lithology effects also made it necessary to use a different criteri-
on for picking Vmax for the clastic formations below the X-unconfor-
mity The velocity at the start of the reversal could not be used, be-
cause this point is in the chalk From pore pressure hindcasts at other
Central North Sea wells, it was decided to set Vmax equal to the nor-
mal trend velocity at the X-unconformity
Fig 14b compares the estimated pressures with mudweights used
during drilling, and RFT data It can be seen that outside the chalk,
the pore pressure estimates are in good agreement with the mea-
sured values However, within the chalk, as was discussed above,
the predictions are essentially a guess
Conclusions
Based on the literature, there appear to be some misconceptions
about fluid expansion as a source of overpressure First, it occurs
more frequently than is generally assumed For instance, undercom-
paction is often cited as the cause of overpressure along the U.S gulf
coast However, velocity-vs.-effective-stress data from this area in-
dicate that fluid expansion mechanisms are an important factor
The second misconception is that fluid expansion overpressure
cannot be estimated from geophysical data It can In fact, a number
of current pore pressure estimation methods have been doing so
without realizing it
Failure to account for the absence or presence of fluid expansion
overpressure can lead to large errors in the estimated pore pressure
Therefore, it is important to have a systematic approach for estimat-
ing pore pressure due to both undercompaction and fluid expansion
Such an approach has been presented It consists of two key ele-
ments: 1) a pair of velocity-vs.-effective-stress relations that ac-
count for overpressure mechanisms besides undercompaction, and
2) a procedure for determining when each relation should be used
Both elements are equally important
Nomenclature
G= effective vertical stress, psi, m/Lt?
v= sonic velocity, ft/sec, L/t
SPE Drilling & Completion, June 1995
Omax = effective vertical stress at the onset of unloading, psi,
m/Lt?
Vmax = sonic velocity at the onset of unloading, ft/sec L/t A,B= virgin curve parameters
U= unloading curve parameter Oye= effective vertical stress at which the sonic velocity intersects the virgin curve, psi, m/Lt?
Snorm = effective vertical stress for normal pore pressure, psi,
m/Lt- Vnorm= sonic velocity for normal pore pressure, ft/sec, L/t C= parameter in Eaton’s implied virgin curve relation Acknowledgments
The author thanks Exxon Production Research Co for permission
to publish this paper Data for the deepwater Gulf of Mexico exam- ple were provided by Exxon Exploration Co., while the Central North Sea well data were received from Shell E&P U.K., and Esso E&P U.K The interpretations of these data are those of the author and not of the organizations furnishing the data
References
1 Foster, J B, and Whalen, J E.: “Estimation of Formation Pressures
From Electrical Surveys Offshore Louisiana,” JPT (Feb 1966), 165
2 Ham, H H.: “A Method of Estimating Formation Pressures From Gulf Coast Well Logs,” Trans., Gulf Coast Assn of Geol Soc., 16, 185-197
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SPEDC
Glenn L Bowers is president of Applied Mechanics Technologies
in Houston, which provides consulting services in abnormal pore pressure, wellbore stability, wellbore fracturing, and general rock mechanics He previously spent 12 years at Exxon Produc- tion Research Co., where he performed research in these same areas He holds BS and MS degrees in mechanical engineering from the U of Akron, and a PhD degree in theoretical and ap-
plied mechanics from the U of Illinois
95