- Email: [email protected]
Compaction and overpressuring in Pleistocene sediments on the Louisiana Shelf, Gulf of Mexico
Marine and Petroleum Geology, Vol. 13, No. 5,
pp. 467-414,
1996
Copyright 0 1996 Elsevier Science Ltd Printed in Great Britain. All rights reserved 0264-8172/96 $15.00+0.00
ELSEVIER
02644172l95)00073-9
Compaction and overpressuring in Pleistocene sediments on the Louisiana Shelf, Gulf of Mexico D. Marc Audet* University of Oxford, Department of Earth Sciences, Parks Road, Oxford OX1 3PR, UK
Received 8 September
1995; accepted in revised form 20 September 1995
Pleistocene shales on the Louisiana Shelf have accumulated at relatively high sedimentation rates (z 1400 m/Ma), resulting in compaction disequilibrium and excess pore pressures. Mathematical models of gravitational compaction are useful tools for quantifying the rates at which various diagenetic processes affect porosity, effective stress and pore pressure. One of the major constraints in compaction modelling is characterising the mechanical compressibility of the sediments under one-dimensional loading. Soil mechanics theory provides a useful framework by quantifying sediment effective stress in terms of two mechanical parameters, both of which can be determined from uniaxial compression tests using a tri-axial apparatus. These mechanical parameters have been measured for natural and remoulded sediments, and many values are published in the geotechnical literature. If mechanical compaction is quantified accurately, then it is possible to distinguish and quantify other porosity reducing mechanisms in sedimentary basins. This paper re-examined published data from two wells in the Eugene Island area ofthe Louisiana Shelf in order to characterize the effective stress behaviour of shale sediments. Mechanical parameters were estimated and found to agree with values from consolidation tests on core samples recovered from nearby sites during Leg 96 of the Deep Sea Drilling Program. Using a continuum mechanics model for gravitational compaction, the estimated mechanical parameters were used to forward model the sudden increase in pore pressure at 2 km burial depth. The modelling results gave a lower bound on the effective permeability ofthe shallow, nearly normally pressured section, and an upper bound for the deeper, overpressured section. The effective permeability in the overpressured section has to be only about 5 times lower than that of the normally pressured section in order to account for the pressure contrast. Theoretical models for the effective permeability of sand-shale mixtures suggest that the permeability difference between the two sections may be due to variations in the shale fraction. Copyright 0 1996 Elsevier Science Ltd. Keywords: compaction;
overpressuring;
Gulf Coast; Pathfinder Well
92”
Introduction Shale deposits on the Louisiana Shelf of the Gulf of Mexico are well known to be overpressured (Dickinson, 1953). Rubey and Hubbert (1959) recognized how the interaction between rapid sediment loading and effective stress could lead to compaction equilibrium. In addition, concurrent mechanisms such as water release due to clay dehydration (smectite illitization) can also be significant (Burst, 1969; Perry and Hower, 1972; Hower et al., 1976; Bruce, 1984), especially at burial depths greater than 23 km. Hart et al. (1995) examined log data from two wells (Well SH #l and Pathfinder Well) in the Eugene Island area of the Louisiana Shelf (Figure I and Figure 2 (a)) and concluded that compaction disequilibrium accounts for about 75% of the observed overpressure. The Pathfinder Well is especially interesting because it passes through a set of fault splays (Figure 2 (b)) at about 2000 m burial depth (corresponding to 1.9 s two-way travel*email: [email protected]
90”
88’
86
28”
28”
26’
26” Site 615.
‘i\\
90’ 88 86’ 81 W Figure 1 Location map of the offshore region of Louisiana (La.) showing bathymetric contours at 200, 2000 and 3000 metres. The shelf break follows approximately the 200 m contour. Sites 615,619 and 621 are from DSDP Leg 96. Well SH #I (Hart eta/., 1995) and the Pathfinder Well are both on the continental shelf, located within 3 km of each other
Marine and Petroleum
Geology 1996 Volume
13 Number 5 467
Compaction
and overpressuring
..,:
STUDY AREA
*QV
331 gH#l
in Pleistocene sediments: D. M. Audet
I
I ..:.:.
k
31°45'W Figure 2 (A) Location of Eugene island 330 (El 330) field, location of Well SH #I and the projected path of the Pathfinder Well. Faults were mapped from GA sand (see B) and the Pathfinder Well appears not to intercept them. (B) Seismic line from three-dimensional survey showing well path for the Pathfinder Well with respect to location of principal stratigraphic (GA, HB, JD, 01 sands) and structural elements (fault splays B, D and A). (After Hart et al., 1995.)
time in Figure 2 (b)). Pressure measurements in the sand bodies cut by the Pathfinder Well show a pressure jump across the fault splays (Hart et al., 1995), which supports the view that the faults restrict pore pressure dissipation. The purpose of this paper is to re-examine the data from Hart et al. (1995) by using soil mechanics theory to improve the characterization of the effective stress. Soil mechanics theory describes the effective stress in terms of two mechanical parameters that can be measured experimentally using a tri-axial apparatus (oedometer). Therefore, effective stress laws deduced from well data can be checked for consistency with data published in the geotechnical and geophysical literature. Porosity-burial depth data from Well SH #I were used to estimate the mechanical parameters describing the effective stress. Using these estimated parameters, a onedimensional gravitational compaction model (Audet and McConnell, 1992) was used to forward model the porosity and pore fluid pressure for the Pathfinder Well. The relatively sharp transition from hydrostatic to high pore pressure at 2000 m burial depth can be explained if the effective permeability of the sediments decreases by a factor of 5-20 at that depth, which may reflect a change in the shale volume fraction, probably due to the juxtaposition of two different sediment structures resulting from movement along the growth fault in the Eugene Island area (Figure 2 (a)).
mechanisms (e.g. pressure solution, cementation) are not involved. For fine-grained sediments, laboratory measurements of ai, and 4 can be correlated by: e 100-e 0: = O,ooexp,, ~
( 1 c,.
where e = $/(l - 4) is the void ratio, (T,~ is some reference value for ok (usually 100 kPa), elOOis the void ratio at a: = 100 kPa, and C, is the compression index. (Note: exp,” x = 1OX.)Equation (2) is based on observations that for sediments subjected to uniform loading, plots of e versus log o: are approximately linear (Skempton, 1944). The effective stress law described by Eq. (2) is often called a normal compression curve. (Skempton referred to C, and eloo as constants of compressibility. In this paper, they are simply called sediment mechanical parameters.) Experimental measurements of C,. and elOOfor clays and natural sediments can be found in the literature (Skempton, 1944; Burland, 1990). The compression index is about 0.1-0.3 for sandy clays and silts, 0.4-0.6 for nonexpandable clays, and 0.7 or greater for colloidal and organic-rich clays. Parasnis (1960) verified Eq. (2) for effective stress levels up to 82 MPa (about 8 km of burial depth). Using an oedometer, Parasnis measured the effective stress laws for a series of natural sediments and showed that C,. and elOOare linearly correlated:
Characterizing sediment compressibility
elOO= 3.37C,,+O.181.
The ability of sediments to sustain mechanical loading is related to the effective stress, o<,,defined by: o:, = 0,-p,,
(1)
where (T”is the vertical stress (overburden) and p, is the pore pressure. Equation (1) is called Terzaghi’s principle of effective stress (Terzaghi, 1936; Atkinson, 1993). For a specified sediment lithology, a: depends only on the porosity, 4, provided that the sediment matrix has not undergone lithification and that other porosity reduction
’
(3)
Equation (3) is a linear regression of the eight data points reported in table 1 (Parasnis, 1960). Based on triaxial tests on remoulded clays, Burland (1990) found that: elOO= 2.02C,. + 0.287.
(4)
Equation (4) is a linear regression of the first 22 data points in table 1 of Burland (1990). Equations (3) and (4) demonstrate that sediment mechanical properties span a relatively small range of values. The main difference
468 Marine and Petroleum Geology 1996 Volume 13 Number 5
Compaction and overpressuring between Eqs (3) and (4) is that the mechanical parameters for calcareous sediments tend to follow Eq. (3) (Audet, 1995a), whereas the mechanical parameters for clays and muds tend to follow Eq. (4). Given a sufficiently large data base, it may be possible to predict C, and elw, which implies that compaction curves can also be predicted.
ments in the shallower sections of Well SH #I are normally pressured, Hart et al. (1995) determined the effective stress by subtracting the hydrostatic pore pressure (based on an assumed hydrostatic pressure gradient of 10.5 MPa/km) from the overburden. Issler (1992) correlated porosity and sonic transit time using the empirical formula:
Compaction of normally pressured sediments
($ =
Sediments can be modelled as a two-component mixture of solids and pore fluid having a bulk density, p, defined by: P = &Jr+(l -$)Ps,
(5)
where 4 is the porosity, pBis the grain density and pI is the pore fluid density. Assuming conditions of zero lateral strain, that is, one-dimensional compression, the overburden is:
ao
2=
ad
+pg,
where g is the acceleration due to gravity and d represents the burial depth measured downward from the depositional surface. For normally pressured sediments, p, is: dP/ z = +Pfg.
in Pleistocene sediments: D. M. Audet
(7)
If a sedimentary column is homogeneous, that is, C,, eloo, pf and ps are independent of d, then Eqs (2) (5)-(7) lead to a theoretical compaction turtle:
+(~)[l+&+r,,],(8) where go is the effective stress at d = 0 (depositional surface) and e, is the void ratio at a: = co calculated from Eq. (2). Equation (8) gives a concise relationship between burial depth d and the porosity 4 (i.e. e). Since by definition there is no fluid flow in normally pressured sediments, there is no need to write down conservation equations that describe the movement of the sediment grains and the pore fluid. Therefore, quantities such as sediment permeability do not enter into Eq. (8). A detailed derivation of Eq. (8) is given by Audet (1995a), who used it to study the mechanical properties of carbonate oozes and chalks on the Ontong Java Plateau, Western Equatorial Pacific. When sediments are overpressured, the fluid flow must be taken into account using Darcy’s Law, and the resulting model is more complicated (Audet and McConnell, 1992; Audet, 1995b).
Soil mechanics analysis of Well SH #l Density, gamma ray and sonic logs are available from Well SH #I ford > 168.5 m. Hart et al. (1995) integrated the density log of Well SH #l to get the overburden (a,). Since the density log was missing for the first 168.5 m of the well, Hart et al. (1995) had to assign a value to the overburden at d = 168.5 m, namely, (T, = 2.241 MPa (Hart, private communication). Assuming that the sedi-
1 _
(!g )y
where At is the log-derived sonic transit time, Atmnis the rock matrix transit time, and x is the acoustic formationfactor exponent. For shales from the BeaufortMackenzie Basin, Issler (1992) found At,, = 220 ps/m and x = 2.19. Hart et al. (1995) used the gamma ray log to identify the shale units, and then used Eq. (9) to derive the shale porosity from the sonic log of Well SH #l. Based on the work of Rubey and Hubbert (1959), Hart et al. (1995) correlated ot, and 4 using:
(10) where fl and & are constants determined by curve fitting. The constant 4r may be interpreted as the porosity at the depositional surface, where cr: is expected to be negligibly small. The disadvantage of Eq. (10) is that /J and & do not correspond directly to parameters measured using consolidation tests, that is, C, and elm. If Eq. (10) gives a good fit to al-- 4 values based on well log data, it cannot be automatically concluded that mechanical compaction is taking place unless the values of /J and 4, determined by curve fitting are consistent with results from laboratory compression tests on the same sediments. In contrast, if data is analysed using Eq. (2), then the resulting values of C, and elOOcan be checked against values available from the soil mechanics, geotechnical literature, and it is then possible to determine how much of the porosity loss is due to mechanical compaction. The ai - I#Idata from Well SH # 1 can be replotted in terms of e versus log ai (Figure 3). The replotted data show a linear fit for 2.5 MPa < g: < 20.45 MPa, the upper limit corresponding approximately to d = 2000 m. The good linear fit (Y = 0.960) suggests that the top 2000 m of the section is normally pressured. Below 2000 m, the data shows no clear trend because 4 starts to increase with increasing burial depth (Figure 4), which means that a: can no longer be calculated by assuming that pf is hydrostatic. The results in Figure 3 show the importance of modelling the effective stress accurately. If the effective stress is modelled using Eq. (IO), as shown in figure 2 from Hart et al. (1995), then it appears that the overpressuring in Well SH #l starts near a{, z 12.5 MPa at a burial depth of 1500 m. Alternatively, using the soil mechanics effective stress law, Eq. (2), the onset of overpressure is located at c: = 20.45 MPa at a burial depth of 2000 m, which is significantly different. The mechanical parameters (C, and eloo) can also be determined by fitting Eq. (8) directly to the 4 -d data from Well SH #I. The best fit of Eq. (8) is shown in Figure 4 (curve B), along with the profile based on the mechanical parameters derived in Figure 3 (curve A). Both profiles agree to within 3%, which means that the density and sonic logs from Well SH #l are self-consist-
Marine and Petroleum
Geology 1996 Volume
13 Number 5 469
Compaction and overpressuring I
I
I
1111
‘j\ ”
in Pleistocene sediments: D. M. Audet
,111
Regression line for Eq. (2)
c,
I
,,,c
=
0.307
-
0.994
-
=
el00
T =
0.8
(4
4
II1’llI’tI1’lll’III’ _
* Site 615 _ [I1Site 619
0.960 3-
o Terzaghi
(1927)
J
0.6e
xWellSH#l
-
el00
2-
OA-
from riverbed
l-
-
gumbo 0 100
w0
10,000 6:
100,000
111,111(111,1,1,111 0.0
0.2
0.4
(kPa)
0.6
0.8
1.0
0.6
0.8
1.0
CC
Figure 3 The effective stress (a:) vs. void ratio (e) from Hart eta/. (1995). The regression line (based on Eq, 2) is fitted to the data points for u: < 20.45 MPa, and ris the regression coefficient. The compression index (C,) and the void ratio at 100 kPa fe,J based on the regression of Eq. (2) are given
I
0
I
I
,
I
I
x Site 621
0 Well
(a:
= 20.45
Parameters
MPa)F ____--_ for
curve (B):
0.0
cc = 0.348 el00
r
0.0
0.1
0.2
0.3
0.4
=
1.104
=
0.948
0.5
0.6
0.7
4 Figure 4 The porosity (4) vs. depth (d) data for Well SH #I from Hart et al. (1995), along with data from Site 621 of DSDP Leg 96 (averaged over 15 m depth intervals). Curve (A) is Eq. (8) using the mechanical parameters CC,and eloO)from Figure 3. Curve KU is the best fit of Eq. (8) to the data from Well SH #I. The values of C, and eloo for curve (6) are given, along with the regression coefficient fr). For both curves (A) and (B), ps = 2700 kg/m3, or = 1050 kg/m3 and o0 = 10 kPa. The dashed line shows the depth corresponding to a:, = 20.45 MPa (see Figure 2)
0.2
0.4
CC Figure 5 Part (a): The correlation of mechanical parameters eloo vs. C,. Equation (3) is the correlation due to Parasnis (1960) for natural sediments and Eq. (4) is the correlation from Burland (1990) for remoulded clays. The mechanical parameters for Well SH #I (from Figs. 3 and 4) are shown, along with values based on consolidation tests on core samples from Sites 615 and 619 of DSDP Leg 96. Also shown are two measurements by Terzaghi (1927) on sediments from the Mississippi region, a gumbo clay and a riverbed clay. Part (b): The compression index from core samples from Sites 615 and 619 versus the burial depth fd) at which the cores were recovered. The vertical line shows the value of C, for Well SH #l, which represents an average value for deeply buried sediments
ent, and that Issler’s calibration curve (Eq. 9) gives acceptable porosity estimates. Figure 4 also shows that Eq. (8) extrapolates well to shallow depths, since curve B matches porosity data from DSDP Site 621 for d < 200 m. In contrast, Hart et al. (1995) using Eq. (lo), found & = 0.4, which is about 20% too low. The estimated mechanical parameters can be compared to the correlations from Parasnis and Burland as shown
in Figure 5 (a). Both estimates of C,. and elOOfor Well SH #I are consistent with Burland’s correlation (Eq. 4) for remoulded clay-rich sediments. Further verification is provided from consolidation tests on core samples recovered from DSDP Sites 615 and 619 on the lower and middle parts of the Mississippi Fan (Bryant et al., 1986a, b). The Mississippi Fan measurements also follow Burland’s correlation (Figure 5 (a)). In addition, Figure 5 (a) shows the mechanical parameters of two sediment samples from the Mississippi region, namely a gumbo clay and a river-bed clay, measured by Terzaghi (1927).
470
13 Number 5
Marine and Petroleum
Geology 1996 Volume
Compaction and overpressuring Terzaghi’s data are also consistent with Burland’s correlation. The C, variation in the DSDP data may be the result of early diagenesis since there is a strong correlation between the core sample burial depth and the compression index (Figure 5 (b)). The mechanical parameters based on core samples from Sites 615 and 619 (70m < d < 90m) bracket the estimates based on Well SH #I. Since the C, estimates from Well SH #l represent the average mechanical behaviour for d > 400 m, it may be concluded that changes in mechanical parameters resulting from early diagenesis are over in the first 100 metres of burial. Early diagenetic alteration of sediment mechanical parameters also takes place in the oozes and chalks in the Costa Rica Rift zone, Eastern Equatorial Pacific Ocean (Wetzel, 1989).
Forward modelling of Pathfinder Well Parameters for the forward model In the previous section, soil mechanics theory was used to estimate mechanical parameters (C, and eloo) for Well SH #I. Since Well SH #l is close to the Pathfinder Well, it may be reasonable to assume that the sediments at the two sites have similar mechanical properties. Therefore, only the effective permeability of the sediments and the sedimentation rate history remain undetermined. However, Audet and McConnell (1992) and Wangen (1992) show that the crucial parameter that controls overpressuring in thick sedimentary columns is the ratio of the hydraulic conductivity to the average sedimentation rate, formally defined in terms of the sedimentation parameter, A: A=!!! p’_l vo ( Pr
)’
(11)
where rcois the nominal value of the sediment hydraulic conductivity at the depositional surface and V0 is the nominal value of the sedimentation rate based on the volume of solid mass evaluated at the surface porosity. The hydraulic conductivity is defined by: kop,g Kg
=
-
P
’
(12)
where k0 is the nominal value of the sediment permeability and p is the pore fluid viscosity. (Note: Wangen (1992) uses the symbol A0 instead of 1.) Equation (11) should not be confused with the 1 used by Rubey and Hubbert (1959) to denote the ratio of the pore pressure to the overburden. To describe the relationship between hydraulic conductivity and porosity, Audet and McConnell (1992) used: K = ~~exp ~(4’ - $02)
(13)
where a is a constant and &ois 4 at d = 0. The data from Olsen (1960) suggest that tl = 14.0. The specific value is not overly crucial to the conclusions of this paper. The other parameters used in the forward model are: c, = 0.348, elm = 1.104, p, = 2700 kg/m3, pf = 1050 kg/m3. Audet and McConnell (1992) used dimensionless variables in their model, which is common practice in applied mathematics. The depth variable is normalized
in Pleistocene sediments: D. M. Audet
by a length scale 2, which is related to the effective stress at the depositional surface, denoted by (T,, according to:
JZ = ,,“b,),
.
(14)
For the forward model, r$ at the depositional surface is denoted by cl in order to distinguish it with (r. used in Eq. (8). The distinction is made for convenience. When using Eq. (8) a0 was set to 10 kPa in order to show the porosity at the shallower depths (Figure 4). If rro = 10 kPa were used in Eq. (14) then the length scale would be about LZ’z 0.62m, which would lead to an inconveniently large number of time steps when modelling the 4 km sediment thickness of the Pathfinder Well. Therefore, the length scale was set to 9 = 50m, corresponding to crl = 809.32 kPa (from Eq. (14)) and & = 0.44071, that is e, = 0.78798 (from Eq. 2) using the values of C,, e,oo, ps and pf stated earlier. The implication of defining a different base for the depositional surface in the forward model is that the model curves from the Audet and McConnell (1992) model have to be shifted in depth so that the depth of 4, is consistent with that derived using Eq. (8). In the simulation runs for the Pathfinder Well, this shift is about 95.35 m (see Figure 6 (a)), which can be verified by evaluating Eq. (8) using e,, (T~= 10 kPa and the appropriate mechanical parameters. Using a constant sedimentation rate, the simulation was run for a dimensionless time of t = 140, which gave a final sediment thickness of about 5.4 km over a period of 5 Ma, assuming V, = 1400 m/Ma (see subsequent section). Results of forward modelling Figure 6 shows the results of using the forward model from Audet and McConnell (1992) to simulate the porosity and the excess pore pressure (JJ~-~,,,~,J of the Pathfinder Well. Using 5 < 1 < 10, it is possible to model the pore pressures in the upper, nearly normally pressured section (d < 2000 m) of the Pathfinder Well (Figure 6 (b)). The deeper, more highly overpressured section (d > 2000 m) can be modelled using 0.25 < I < 0.5. The associated porosity profiles (Figure 6 (a)) show that the porosity range at the bottom of the normally pressured section (1900 m) of the Pathfinder Well is consistent with the porosity data from the normally pressured section from Well SH #l . Figure 6 (a) also shows the theoretical compaction curve and the forward model curves for 1 = 0.25-10. At the top of the overpressured section (2200 m), the porosity of the Pathfinder Well is more consistent with I = 1 (in contrast to 0.25 < A < 0.5 for the excess pore pressure). This suggests that if the porosity data are accurate, then some secondary mechanism is contributing to the excess pore pressure below 2000 m in the Pathfinder Well, in keeping with the conclusions from Hart et al. (1995) and the theoretical results from Audet (1995b). The model from Audet and McConnell (1992) assumes a sedimentary column with homogeneous physical properties. The simulated results shown in Figure 6 clearly do not model the sharp pore pressure increase at d = 2000 m. However, this is not a serious limitation because of the following reasons. For the nearly normally pressured cases (1 = 5, lo), the pressure and porosity in the top 2 km of the column will be approximately the same, regardless of whether or not the underlying section
Marine and Petroleum
Geology 1996 Volume
13 Number 5 471
Compaction and over-pressuring
in Pleistocene
D. M. Audet
sediments:
IIISkempton (1944)
- HPathfinder Well
0.6
iP
??
[11 ‘\Well
SH #l
(Cc = 0.348) 1
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0
20
40
4
in Above
B Fault
X Below A Fault lithostatic
\\
80
100
Figure 7 The compression index (CJ as a function of the percent clay fraction. The clay fraction consists of particles with equivalent diameters less than 2 pm. The data (Skempton, 1944) shows that C, is proportional to clay content. The horizontal line shows the clay fraction range where the C, estimate for Well SH #I is likely to be found
(b) ~~~~~~‘ “~““~“~~~“ ~~~‘ ~ Pathfinder Well: \ ‘\,~Excess
60
% Clay fraction
(12.324
gradient:
MPa/km)
The effective permeability of Gulf Coast shales
0
10
30
20 Pf
-
40
50
Phydro
PW
Figure 6 Forward modelling of porosity (4) (a) and excess pore fluid pressure (or-ohvdro ) (b) for the Pathfinder Well. Part (a) shows the best fit of Eq. (8) (curve 6 from Figure 41, along with simulated porosity profiles for I = 0.25,0.5, I,5 and 10 (note the 95.35 m shift in the origin). Porosity data from the Pathfinder Well are shown at d = 1900 m (bottom of normally pressured section). Porosity section) and d= 2200 m (top of overpressured data from Well SH #I are shown for comparison. Part (b) shows the corresponding excess pore pressure profiles for 0.25 < d < 10. The excess lithostatic gradient (dashed line) is based on a reference lithostatic gradient of 22.621 MPalkm (1 psi/ft) and a hydrostatic gradient 10.297 MPa/km. Measurements for the Pathfinder Well are ;Prom Hart et al. (1995) taken above the B Fault and below the A Fault (see Figure 2b)
at d > 2 km is overpressured. Therefore, when modelling the top 2 km of the section, the variations in permeability at greater depth do not have to be taken into account in a first order model. Alternatively, when modelling the overpressured section at d > 2 km (1 = 0.25, 0.5, l), the excess pore pressure is controlled primarily by the permeability of the overpressured section and a detailed model of the more highly permeable overlying section is not needed. In principle, a more sophisticated model that takes into account changes in permeability due to lithology could be developed, but it is not strictly necessary for the results of this paper.
472
Marine and Petroleum
Geology 1996 Volume
The results of the forward model suggest a lower bound for the effective hydraulic conductivity of the Pathfinder Well sediments. In the Eugene Island area of the Gulf Coast, Pleistocene deposits (1.6 Ma) may be as much as 2.2 km thick (Galloway et al., 199I), suggesting an average sedimentation rate of about V, =2200/1.6= 1375 m/Ma, but this could vary by a factor of 5 or 10. Assuming I”’ = 1400 m/Ma, the effective hydraulic conductivity of the normally pressured sediments in the first 2000 m of the Pathfinder Well must be at least KO x 13 * lop9 cm/s, that is, using Eq. (11) with i = 5: -1 = 5*1,40OmMa-’ lOOcmm_’ ’ 3.15*10’3sMap’
2,70Okgm- _ 1 -’ 1,05Okgm-’
= 13 * l(pE. S
Likewise, in the overpressured section below 2000 m, the effective hydraulic conductivity can be no larger than ‘coz 2.6. 10d9 cm/s (using ;1 = 1). Therefore, regardless of the exact value of V. or the absolute value of ice, the transition from near hydrostatic pore pressures to high pore pressures at d = 2000 m of the Pathfinder Well can be explained by a reduction of hydraulic conductivity by a factor of 5. It is worth considering an alternative explanation for the pressure change at 2000 m in the Pathfinder Well. Instead of having a factor of 5 difference in the effective permeability, there could be a factor of 5 difference in the average sedimentation rate between the sediments above and below the fault splays in the Pathfinder Well. For purposes of illustration, consider first the case where the
13 Number 5
Compaction and overpressuring overpressured section (d > 2000 m) has been deposited at VO = 1400 m/Ma. By implication, in the shallower section the deposition rate must be 5 times lower, V, = 280 m/Ma, which means that it took at least 7.14 Ma to fill in the present-day section. Since the Pleistocene is about 1.6 Ma, there would not have been enough time for this scenario to take place. Alternatively, if the average sedimentation rate of the shallower section is V,, = 1400 m/Ma, then the rate in the deeper, overpressured section must be about V, = 7000 m/Ma, which is a very high number. According to figure 1 from Sadler (1981), most sediment accumulation rates are in the range 5 m/Ma < V, < 2000 m/Ma over 1 Ma time scales. Without biostratigraphic evidence from the Pathfinder Well, it would be hard to accept such a high value of V,,.In light of the available data, it is much easier to postulate a 5-fold change in permeability than a 5-fold change in average sedimentation rate. McCarthy (199 1) modelled the effective permeability of sand-shale mixtures by simulating fluid flow in a three dimensional composite material consisting of bodies of relatively impermeable material (i.e. shale inclusions) randomly embedded in a matrix of permeable material (i.e. sandstone matrix). The shale inclusions are spheroidal in shape with an anisotropy ratio 6 (ratio of major to minor axis). The numerical results were correlated using: k* = k,,(l -f)““,
(15)
where k,, is the sand permeability, f is the shale volume fraction, k* is the effective permeability of the sand-shale mixture and m is an exponent. McCarthy gave upper and lower bounds for m as a function of E. The upper and lower bounds account for the effects of the alignment of the spheroidal inclusions and differences between horizontal permeability (in the flow direction) and vertical permeability (perpendicular to the flow direction). Let kg and k;S be the effective permeabilities of the sediments in the normal and overpressured sections, respectively, and fNand f0 be the corresponding shale volume fractions. Using Eq. (15), consider the ratio of k$ to k::
(16) If the ratio k$/k,$ is specified, then for a given value offN the corresponding value of f. can be calculated. Rearranging Eq. (16) gives: fo=
;
1-(1-f,) 0
-Y
(17)
For example, assuming that k$/kg = 5, fN = 0.5 and m = 0.05, then f0 = 0.539 (see the first column of Table I). This example using the McCarthy model says that if the shale fraction in the normally pressured section is 50%, then the shale fraction in the overpressured section only has to increase by 3.9% (i.e. 53.9%) to decrease the effective permeability by a factor of 5. Table I shows f0 calculated using Eq. (17) for 0.4 < fN $ 0.6, a range consistent with results from DSDP Leg 96 (Stow et al., 1986). Depending on the exact value oft used, increasing fNby 0.03-0.20 can decrease kg by a factor of 5, which could account for the observed pore pressure change in the Pathfinder Well.
in Pleistocene sediments: D. M. Audet
Table 1 The shale fraction volume of the overpressured section Cfd required to give a permeability reduction kg/k+, = l/5 for a given shale fraction of the normally pressured section ( fN), based on the effective permeability model of McCarthy (1991). E is the anisotropy ratio of the spheroidal geometry used to model the shale inclusions. mlow and mop are lower and upper bounds for the exponent m in Eq. (15) (see table 2, McCarthy, 1991) f,forc=30 fN
mlow= 0.05
0.4 0.5 0.6
0.446 0.539 0.631
f,fort=lO m,,=0.13
0.513 0.594 0.675
m,0,=0.14 0.522 0.601 0.681
m,=0.25
0.599 0.666 0.732
If the effective permeability of the Gulf Coast sediments depends on the shale volume fraction, then the mechanical properties probably also depend on the shale content. Figure 8 shows the compression index, C,, as a function of clay fraction, defined as the percentage of sediment volume having an equivalent diameter less than 2 pm. In general, the compression index increases as the clay fraction increases. For C, = 0.348, the value for Well SH #l derived from log data, the sediment clay fraction could easily be between 20% and 45%. In the previous section, the same value of C’,was used to model both the shallower, normally pressured section and the deeper, overpressired section. This simplifying assumption is probably justified since the the scattered data in Figure 8 show that C, may not vary all that much with modest (1@30%) variations in clay (shale) fraction.
Discussion and conclusions Mud rich sediments in the Eugene Island area of the Louisiana Shelf show a normally pressured section about 2 km thick overlying an overpressured section. Using soil mechanics theory, the mechanical parameters (C, and el,,,) of the normally pressured sediments were estimated and found to be consistent with the results of consolidation tests made on Mississippi Fan sediments recovered during DSDP Leg 96, and with the general correlation for remoulded clays (Burland, 1990). The compaction curve based on the soil mechanics effective stress law is able to match the higher sediment porosities near the depositional surface, unlike the exponential law used by Hart et al. (1995). To fully appreciate how sediments compact at depth, it is useful to understand mechanical compaction in the early stages of burial. Since mechanical compaction is a major control on overpressure development, the effective stress must be modelled accurately, otherwise the onset of overpressuring can be mislocated by as much as 500 m, as shown for the case of Well SH #I. Using a one-dimensional compaction model (Audet and McConnell, 1992), porosities and pressure profiles for the Pathfinder Well were simulated. The excess pore pressures can be modelled provided that the sedimentation parameter is 0.25 < 1 < 1, suggesting that the effective permeability of the sediments in the overpressured zone is at least 5 times lower than that in the nearly normally pressured section (which can be modelled with 5 < /z < 10). The effective permeability model of McCarthy (1991) indicates that increasing the shale volume fraction by 3-20% could account for the decrease
Marine and Petroleum
Geology 1996 Volume
13 Number 5 473
Compaction and overpressuring
in Pleistocene sediments: 0. M. Audet
in permeability, suggesting that the top of the overpressured section is partially determined by stratigraphic factors related to the depositional environment of the sediments. The use of density and sonic logs, along with Issler’s (Issler, 1992) calibration curve, appears to provide a consistent framework for analysing effective stress, porosity and pore pressure in shale layers. Combined with soil mechanics theory, well log data can be used to better constrain mechanical compaction in forward basin models and to improve the understanding of excess pore pressure development.
Acknowledgements This work was supported by Amoco (UK) Exploration Company. The author thanks Peter Flemings and Bruce Hart for providing a preprint of Hart et al. (1995) and for useful comments on the manuscript.
References Atkinson, J. (1993) An introduction to the Mechanics ofSoils and Foundations, McGraw-Hill, London. Audet, D. M. (1995a) Modelling of porosity evolution and mechanical compaction of calcareous sediments Sedimenfology 42,355-373. Audet, D. M. (1995b3 Mathematical modelling of gravitational compaction and clay dehydration in thick sediment layers Geophys. J. Int. 122,283-298. Audet, D. M. and McConnell, J. D. C. (1992) Forward modelling of porosity and pore pressure evolution in sedimentary basins Basin Res. 4, 147-162. Bruce, C. H. (1984) Smectite Dehydration-its relation to structural development and hydrocarbon accumulation in northern Gulf of Mexico Basin AAPG Bulletin 68, 673-683. Bryant, W., Wetzel, A. and Sweet, W. (1986a) Geotechnical properties of intraslope basin sediments, Gulf of Mexico, De@o Sea Drillina Proiect Lea 96. Site 619. In: Init. Reefs. DSDP J. c. Coleman, A. W. Meier et al.) 96 (ids A. H. Biumi, Washington (U.S. Govt. Printing Office), 819-824. Bryant, W., Wetzel, A., Taylor, E. and Sweet, W. (1986b) Consolidation characteristics and permeability of Mississippi Fan sediments. In: /nit. Reefs. DSDP 96 (Eds A. H. Bouma. J. M. Coleman, A. W. Meyer’ef al.) Washington (U.S. Govt. Piinting Office), 797-809. Burland, J. B. (1990) On the compressibility and shear strength of natural clays Ggotechnique 40,329-378. Burst, J. F. (1969) Diagenesis of Gulf Coast clayey sediments and
its possible relation to petroleum migration AAPG Bulletin 53,73-93. Dickinson, G. (1953) Geological aspects of abnormal reservoir pressures in Gulf Coast Louisiana AAPG Sulletin37,410-432. Galloway, W. E., Bebout, D. G., Fisher, W. L., Dunlap, J. B. Jr, Cabrera-Castro, IX, Lugo-Rivera, J. E. and Scott, T. M. (1991) Cenozoic, In: The Gulf of Mexico Basin. (Ed. A. Salvador) Boulder, Colorado, Geological Society of America, The Geology of North America, v. J, 245-324. Hart, B. S., Flemings, P. B. and Deshpande, A. (1995) Porosity and pressure: role of compaction disequilibrium in the development of geopressures in a Gulf Coast Pleistocene basin Geology 23,45-48. Hower, J., Eslinger, E. V., Hower, M. E. and Perry, E. A. (1976) Mechanism of burial metamorphism of argillaceous sediment: I. Mineralogical and chemical evidence GSA Bulletin 87,725-737. Issler, D. R. (1992) A new approach to shale compaction and stratigraphic restoration, Beaufort-Mackenzie Basin and Mackenzie Corridor, Northern Canada AAPG Bulletin 76, 1170-1189. McCarthy, J. F. (1991) Analytical models of the effective permeability of sand-shale reservoirs Geophys. J. Inf. 105, 513527. Olsen, H. W. (1960) Hydraulic flow through saturated clays Clays ClayMineralsll, 131-161. Parasnis, D. S. (1960) The compaction of sediments and its bearing on some geophysical problems Geophys. J. Roy. Astron. Sot. 3, l-28. Perry, E. A. Jr and Hower, J. (1972) Late-stage dehydration in deeply buried pelitic sediments AAPG Bulletin 56,2013-2021. Rubey, W. W. and Hubbert, M. K. (1959) Role of fluid pressure in mechanics of overthrust faulting: II. overthrust belt in geosynclinal area of Western Wyoming in light of fluid-pressure hypothesis GSA Bulletin 70, 167-206. Sadler, P. M. (1981) Sediment accumulation rates and the completeness of stratigraphic sections J. Geol. 89, 569-584. Skempton, A. W. (1944) Notes on the compressibility of clays 0. J. geol. Sot. Lond. 100, 119-135. Stow, D. A. V., Cremer, M., Droz, L., Meyer, A. W., Normark, W. R., O’Connell, S., Pickering, K. T., Stelting, C. E., Angell, S. A. and Chaplin, C. (1986) Facies, composition and texture of Mississippi Fan sediments, Deep Sea Drilling Project Leg 96, Gulf of Mexico. In: /nit. Repts. DSDP 96 (Eds A. H. Bouma, J. M. Coleman, A. W. Meyer et al.) Washington (U.S. Govt. Printing Office), 475-487. Terzaghi, K. (1927) Principles of final soil classification Public Roads8,41. Terzaghi, K. (1936) The shearing resistance of saturated soil and the angle between the planes of shear. In: froc. of Ist International S/WE Conference. Harvard, Mass. 1, 54-56. Wangen, M. (1992) Pressure and temperature evolution in sedimentary basins Geophys. J. Int. 110,601-613. Wetzel, A. (1989) Influence of heat flow on ooze/chalk cementation: quantification from consolidation parameters in DSDP Sites 504 and 505 sediments J. Sediment. Petrol. 59,539-547.
474 Marine and Petroleum Geology 1996 Volume 13 Number 5
pp. 467-414,
1996
Copyright 0 1996 Elsevier Science Ltd Printed in Great Britain. All rights reserved 0264-8172/96 $15.00+0.00
ELSEVIER
02644172l95)00073-9
Compaction and overpressuring in Pleistocene sediments on the Louisiana Shelf, Gulf of Mexico D. Marc Audet* University of Oxford, Department of Earth Sciences, Parks Road, Oxford OX1 3PR, UK
Received 8 September
1995; accepted in revised form 20 September 1995
Pleistocene shales on the Louisiana Shelf have accumulated at relatively high sedimentation rates (z 1400 m/Ma), resulting in compaction disequilibrium and excess pore pressures. Mathematical models of gravitational compaction are useful tools for quantifying the rates at which various diagenetic processes affect porosity, effective stress and pore pressure. One of the major constraints in compaction modelling is characterising the mechanical compressibility of the sediments under one-dimensional loading. Soil mechanics theory provides a useful framework by quantifying sediment effective stress in terms of two mechanical parameters, both of which can be determined from uniaxial compression tests using a tri-axial apparatus. These mechanical parameters have been measured for natural and remoulded sediments, and many values are published in the geotechnical literature. If mechanical compaction is quantified accurately, then it is possible to distinguish and quantify other porosity reducing mechanisms in sedimentary basins. This paper re-examined published data from two wells in the Eugene Island area ofthe Louisiana Shelf in order to characterize the effective stress behaviour of shale sediments. Mechanical parameters were estimated and found to agree with values from consolidation tests on core samples recovered from nearby sites during Leg 96 of the Deep Sea Drilling Program. Using a continuum mechanics model for gravitational compaction, the estimated mechanical parameters were used to forward model the sudden increase in pore pressure at 2 km burial depth. The modelling results gave a lower bound on the effective permeability ofthe shallow, nearly normally pressured section, and an upper bound for the deeper, overpressured section. The effective permeability in the overpressured section has to be only about 5 times lower than that of the normally pressured section in order to account for the pressure contrast. Theoretical models for the effective permeability of sand-shale mixtures suggest that the permeability difference between the two sections may be due to variations in the shale fraction. Copyright 0 1996 Elsevier Science Ltd. Keywords: compaction;
overpressuring;
Gulf Coast; Pathfinder Well
92”
Introduction Shale deposits on the Louisiana Shelf of the Gulf of Mexico are well known to be overpressured (Dickinson, 1953). Rubey and Hubbert (1959) recognized how the interaction between rapid sediment loading and effective stress could lead to compaction equilibrium. In addition, concurrent mechanisms such as water release due to clay dehydration (smectite illitization) can also be significant (Burst, 1969; Perry and Hower, 1972; Hower et al., 1976; Bruce, 1984), especially at burial depths greater than 23 km. Hart et al. (1995) examined log data from two wells (Well SH #l and Pathfinder Well) in the Eugene Island area of the Louisiana Shelf (Figure I and Figure 2 (a)) and concluded that compaction disequilibrium accounts for about 75% of the observed overpressure. The Pathfinder Well is especially interesting because it passes through a set of fault splays (Figure 2 (b)) at about 2000 m burial depth (corresponding to 1.9 s two-way travel*email: [email protected]
90”
88’
86
28”
28”
26’
26” Site 615.
‘i\\
90’ 88 86’ 81 W Figure 1 Location map of the offshore region of Louisiana (La.) showing bathymetric contours at 200, 2000 and 3000 metres. The shelf break follows approximately the 200 m contour. Sites 615,619 and 621 are from DSDP Leg 96. Well SH #I (Hart eta/., 1995) and the Pathfinder Well are both on the continental shelf, located within 3 km of each other
Marine and Petroleum
Geology 1996 Volume
13 Number 5 467
Compaction
and overpressuring
..,:
STUDY AREA
*QV
331 gH#l
in Pleistocene sediments: D. M. Audet
I
I ..:.:.
k
31°45'W Figure 2 (A) Location of Eugene island 330 (El 330) field, location of Well SH #I and the projected path of the Pathfinder Well. Faults were mapped from GA sand (see B) and the Pathfinder Well appears not to intercept them. (B) Seismic line from three-dimensional survey showing well path for the Pathfinder Well with respect to location of principal stratigraphic (GA, HB, JD, 01 sands) and structural elements (fault splays B, D and A). (After Hart et al., 1995.)
time in Figure 2 (b)). Pressure measurements in the sand bodies cut by the Pathfinder Well show a pressure jump across the fault splays (Hart et al., 1995), which supports the view that the faults restrict pore pressure dissipation. The purpose of this paper is to re-examine the data from Hart et al. (1995) by using soil mechanics theory to improve the characterization of the effective stress. Soil mechanics theory describes the effective stress in terms of two mechanical parameters that can be measured experimentally using a tri-axial apparatus (oedometer). Therefore, effective stress laws deduced from well data can be checked for consistency with data published in the geotechnical and geophysical literature. Porosity-burial depth data from Well SH #I were used to estimate the mechanical parameters describing the effective stress. Using these estimated parameters, a onedimensional gravitational compaction model (Audet and McConnell, 1992) was used to forward model the porosity and pore fluid pressure for the Pathfinder Well. The relatively sharp transition from hydrostatic to high pore pressure at 2000 m burial depth can be explained if the effective permeability of the sediments decreases by a factor of 5-20 at that depth, which may reflect a change in the shale volume fraction, probably due to the juxtaposition of two different sediment structures resulting from movement along the growth fault in the Eugene Island area (Figure 2 (a)).
mechanisms (e.g. pressure solution, cementation) are not involved. For fine-grained sediments, laboratory measurements of ai, and 4 can be correlated by: e 100-e 0: = O,ooexp,, ~
( 1 c,.
where e = $/(l - 4) is the void ratio, (T,~ is some reference value for ok (usually 100 kPa), elOOis the void ratio at a: = 100 kPa, and C, is the compression index. (Note: exp,” x = 1OX.)Equation (2) is based on observations that for sediments subjected to uniform loading, plots of e versus log o: are approximately linear (Skempton, 1944). The effective stress law described by Eq. (2) is often called a normal compression curve. (Skempton referred to C, and eloo as constants of compressibility. In this paper, they are simply called sediment mechanical parameters.) Experimental measurements of C,. and elOOfor clays and natural sediments can be found in the literature (Skempton, 1944; Burland, 1990). The compression index is about 0.1-0.3 for sandy clays and silts, 0.4-0.6 for nonexpandable clays, and 0.7 or greater for colloidal and organic-rich clays. Parasnis (1960) verified Eq. (2) for effective stress levels up to 82 MPa (about 8 km of burial depth). Using an oedometer, Parasnis measured the effective stress laws for a series of natural sediments and showed that C,. and elOOare linearly correlated:
Characterizing sediment compressibility
elOO= 3.37C,,+O.181.
The ability of sediments to sustain mechanical loading is related to the effective stress, o<,,defined by: o:, = 0,-p,,
(1)
where (T”is the vertical stress (overburden) and p, is the pore pressure. Equation (1) is called Terzaghi’s principle of effective stress (Terzaghi, 1936; Atkinson, 1993). For a specified sediment lithology, a: depends only on the porosity, 4, provided that the sediment matrix has not undergone lithification and that other porosity reduction
’
(3)
Equation (3) is a linear regression of the eight data points reported in table 1 (Parasnis, 1960). Based on triaxial tests on remoulded clays, Burland (1990) found that: elOO= 2.02C,. + 0.287.
(4)
Equation (4) is a linear regression of the first 22 data points in table 1 of Burland (1990). Equations (3) and (4) demonstrate that sediment mechanical properties span a relatively small range of values. The main difference
468 Marine and Petroleum Geology 1996 Volume 13 Number 5
Compaction and overpressuring between Eqs (3) and (4) is that the mechanical parameters for calcareous sediments tend to follow Eq. (3) (Audet, 1995a), whereas the mechanical parameters for clays and muds tend to follow Eq. (4). Given a sufficiently large data base, it may be possible to predict C, and elw, which implies that compaction curves can also be predicted.
ments in the shallower sections of Well SH #I are normally pressured, Hart et al. (1995) determined the effective stress by subtracting the hydrostatic pore pressure (based on an assumed hydrostatic pressure gradient of 10.5 MPa/km) from the overburden. Issler (1992) correlated porosity and sonic transit time using the empirical formula:
Compaction of normally pressured sediments
($ =
Sediments can be modelled as a two-component mixture of solids and pore fluid having a bulk density, p, defined by: P = &Jr+(l -$)Ps,
(5)
where 4 is the porosity, pBis the grain density and pI is the pore fluid density. Assuming conditions of zero lateral strain, that is, one-dimensional compression, the overburden is:
ao
2=
ad
+pg,
where g is the acceleration due to gravity and d represents the burial depth measured downward from the depositional surface. For normally pressured sediments, p, is: dP/ z = +Pfg.
in Pleistocene sediments: D. M. Audet
(7)
If a sedimentary column is homogeneous, that is, C,, eloo, pf and ps are independent of d, then Eqs (2) (5)-(7) lead to a theoretical compaction turtle:
+(~)[l+&+r,,],(8) where go is the effective stress at d = 0 (depositional surface) and e, is the void ratio at a: = co calculated from Eq. (2). Equation (8) gives a concise relationship between burial depth d and the porosity 4 (i.e. e). Since by definition there is no fluid flow in normally pressured sediments, there is no need to write down conservation equations that describe the movement of the sediment grains and the pore fluid. Therefore, quantities such as sediment permeability do not enter into Eq. (8). A detailed derivation of Eq. (8) is given by Audet (1995a), who used it to study the mechanical properties of carbonate oozes and chalks on the Ontong Java Plateau, Western Equatorial Pacific. When sediments are overpressured, the fluid flow must be taken into account using Darcy’s Law, and the resulting model is more complicated (Audet and McConnell, 1992; Audet, 1995b).
Soil mechanics analysis of Well SH #l Density, gamma ray and sonic logs are available from Well SH #I ford > 168.5 m. Hart et al. (1995) integrated the density log of Well SH #l to get the overburden (a,). Since the density log was missing for the first 168.5 m of the well, Hart et al. (1995) had to assign a value to the overburden at d = 168.5 m, namely, (T, = 2.241 MPa (Hart, private communication). Assuming that the sedi-
1 _
(!g )y
where At is the log-derived sonic transit time, Atmnis the rock matrix transit time, and x is the acoustic formationfactor exponent. For shales from the BeaufortMackenzie Basin, Issler (1992) found At,, = 220 ps/m and x = 2.19. Hart et al. (1995) used the gamma ray log to identify the shale units, and then used Eq. (9) to derive the shale porosity from the sonic log of Well SH #l. Based on the work of Rubey and Hubbert (1959), Hart et al. (1995) correlated ot, and 4 using:
(10) where fl and & are constants determined by curve fitting. The constant 4r may be interpreted as the porosity at the depositional surface, where cr: is expected to be negligibly small. The disadvantage of Eq. (10) is that /J and & do not correspond directly to parameters measured using consolidation tests, that is, C, and elm. If Eq. (10) gives a good fit to al-- 4 values based on well log data, it cannot be automatically concluded that mechanical compaction is taking place unless the values of /J and 4, determined by curve fitting are consistent with results from laboratory compression tests on the same sediments. In contrast, if data is analysed using Eq. (2), then the resulting values of C, and elOOcan be checked against values available from the soil mechanics, geotechnical literature, and it is then possible to determine how much of the porosity loss is due to mechanical compaction. The ai - I#Idata from Well SH # 1 can be replotted in terms of e versus log ai (Figure 3). The replotted data show a linear fit for 2.5 MPa < g: < 20.45 MPa, the upper limit corresponding approximately to d = 2000 m. The good linear fit (Y = 0.960) suggests that the top 2000 m of the section is normally pressured. Below 2000 m, the data shows no clear trend because 4 starts to increase with increasing burial depth (Figure 4), which means that a: can no longer be calculated by assuming that pf is hydrostatic. The results in Figure 3 show the importance of modelling the effective stress accurately. If the effective stress is modelled using Eq. (IO), as shown in figure 2 from Hart et al. (1995), then it appears that the overpressuring in Well SH #l starts near a{, z 12.5 MPa at a burial depth of 1500 m. Alternatively, using the soil mechanics effective stress law, Eq. (2), the onset of overpressure is located at c: = 20.45 MPa at a burial depth of 2000 m, which is significantly different. The mechanical parameters (C, and eloo) can also be determined by fitting Eq. (8) directly to the 4 -d data from Well SH #I. The best fit of Eq. (8) is shown in Figure 4 (curve B), along with the profile based on the mechanical parameters derived in Figure 3 (curve A). Both profiles agree to within 3%, which means that the density and sonic logs from Well SH #l are self-consist-
Marine and Petroleum
Geology 1996 Volume
13 Number 5 469
Compaction and overpressuring I
I
I
1111
‘j\ ”
in Pleistocene sediments: D. M. Audet
,111
Regression line for Eq. (2)
c,
I
,,,c
=
0.307
-
0.994
-
=
el00
T =
0.8
(4
4
II1’llI’tI1’lll’III’ _
* Site 615 _ [I1Site 619
0.960 3-
o Terzaghi
(1927)
J
0.6e
xWellSH#l
-
el00
2-
OA-
from riverbed
l-
-
gumbo 0 100
w0
10,000 6:
100,000
111,111(111,1,1,111 0.0
0.2
0.4
(kPa)
0.6
0.8
1.0
0.6
0.8
1.0
CC
Figure 3 The effective stress (a:) vs. void ratio (e) from Hart eta/. (1995). The regression line (based on Eq, 2) is fitted to the data points for u: < 20.45 MPa, and ris the regression coefficient. The compression index (C,) and the void ratio at 100 kPa fe,J based on the regression of Eq. (2) are given
I
0
I
I
,
I
I
x Site 621
0 Well
(a:
= 20.45
Parameters
MPa)F ____--_ for
curve (B):
0.0
cc = 0.348 el00
r
0.0
0.1
0.2
0.3
0.4
=
1.104
=
0.948
0.5
0.6
0.7
4 Figure 4 The porosity (4) vs. depth (d) data for Well SH #I from Hart et al. (1995), along with data from Site 621 of DSDP Leg 96 (averaged over 15 m depth intervals). Curve (A) is Eq. (8) using the mechanical parameters CC,and eloO)from Figure 3. Curve KU is the best fit of Eq. (8) to the data from Well SH #I. The values of C, and eloo for curve (6) are given, along with the regression coefficient fr). For both curves (A) and (B), ps = 2700 kg/m3, or = 1050 kg/m3 and o0 = 10 kPa. The dashed line shows the depth corresponding to a:, = 20.45 MPa (see Figure 2)
0.2
0.4
CC Figure 5 Part (a): The correlation of mechanical parameters eloo vs. C,. Equation (3) is the correlation due to Parasnis (1960) for natural sediments and Eq. (4) is the correlation from Burland (1990) for remoulded clays. The mechanical parameters for Well SH #I (from Figs. 3 and 4) are shown, along with values based on consolidation tests on core samples from Sites 615 and 619 of DSDP Leg 96. Also shown are two measurements by Terzaghi (1927) on sediments from the Mississippi region, a gumbo clay and a riverbed clay. Part (b): The compression index from core samples from Sites 615 and 619 versus the burial depth fd) at which the cores were recovered. The vertical line shows the value of C, for Well SH #l, which represents an average value for deeply buried sediments
ent, and that Issler’s calibration curve (Eq. 9) gives acceptable porosity estimates. Figure 4 also shows that Eq. (8) extrapolates well to shallow depths, since curve B matches porosity data from DSDP Site 621 for d < 200 m. In contrast, Hart et al. (1995) using Eq. (lo), found & = 0.4, which is about 20% too low. The estimated mechanical parameters can be compared to the correlations from Parasnis and Burland as shown
in Figure 5 (a). Both estimates of C,. and elOOfor Well SH #I are consistent with Burland’s correlation (Eq. 4) for remoulded clay-rich sediments. Further verification is provided from consolidation tests on core samples recovered from DSDP Sites 615 and 619 on the lower and middle parts of the Mississippi Fan (Bryant et al., 1986a, b). The Mississippi Fan measurements also follow Burland’s correlation (Figure 5 (a)). In addition, Figure 5 (a) shows the mechanical parameters of two sediment samples from the Mississippi region, namely a gumbo clay and a river-bed clay, measured by Terzaghi (1927).
470
13 Number 5
Marine and Petroleum
Geology 1996 Volume
Compaction and overpressuring Terzaghi’s data are also consistent with Burland’s correlation. The C, variation in the DSDP data may be the result of early diagenesis since there is a strong correlation between the core sample burial depth and the compression index (Figure 5 (b)). The mechanical parameters based on core samples from Sites 615 and 619 (70m < d < 90m) bracket the estimates based on Well SH #I. Since the C, estimates from Well SH #l represent the average mechanical behaviour for d > 400 m, it may be concluded that changes in mechanical parameters resulting from early diagenesis are over in the first 100 metres of burial. Early diagenetic alteration of sediment mechanical parameters also takes place in the oozes and chalks in the Costa Rica Rift zone, Eastern Equatorial Pacific Ocean (Wetzel, 1989).
Forward modelling of Pathfinder Well Parameters for the forward model In the previous section, soil mechanics theory was used to estimate mechanical parameters (C, and eloo) for Well SH #I. Since Well SH #l is close to the Pathfinder Well, it may be reasonable to assume that the sediments at the two sites have similar mechanical properties. Therefore, only the effective permeability of the sediments and the sedimentation rate history remain undetermined. However, Audet and McConnell (1992) and Wangen (1992) show that the crucial parameter that controls overpressuring in thick sedimentary columns is the ratio of the hydraulic conductivity to the average sedimentation rate, formally defined in terms of the sedimentation parameter, A: A=!!! p’_l vo ( Pr
)’
(11)
where rcois the nominal value of the sediment hydraulic conductivity at the depositional surface and V0 is the nominal value of the sedimentation rate based on the volume of solid mass evaluated at the surface porosity. The hydraulic conductivity is defined by: kop,g Kg
=
-
P
’
(12)
where k0 is the nominal value of the sediment permeability and p is the pore fluid viscosity. (Note: Wangen (1992) uses the symbol A0 instead of 1.) Equation (11) should not be confused with the 1 used by Rubey and Hubbert (1959) to denote the ratio of the pore pressure to the overburden. To describe the relationship between hydraulic conductivity and porosity, Audet and McConnell (1992) used: K = ~~exp ~(4’ - $02)
(13)
where a is a constant and &ois 4 at d = 0. The data from Olsen (1960) suggest that tl = 14.0. The specific value is not overly crucial to the conclusions of this paper. The other parameters used in the forward model are: c, = 0.348, elm = 1.104, p, = 2700 kg/m3, pf = 1050 kg/m3. Audet and McConnell (1992) used dimensionless variables in their model, which is common practice in applied mathematics. The depth variable is normalized
in Pleistocene sediments: D. M. Audet
by a length scale 2, which is related to the effective stress at the depositional surface, denoted by (T,, according to:
JZ = ,,“b,),
.
(14)
For the forward model, r$ at the depositional surface is denoted by cl in order to distinguish it with (r. used in Eq. (8). The distinction is made for convenience. When using Eq. (8) a0 was set to 10 kPa in order to show the porosity at the shallower depths (Figure 4). If rro = 10 kPa were used in Eq. (14) then the length scale would be about LZ’z 0.62m, which would lead to an inconveniently large number of time steps when modelling the 4 km sediment thickness of the Pathfinder Well. Therefore, the length scale was set to 9 = 50m, corresponding to crl = 809.32 kPa (from Eq. (14)) and & = 0.44071, that is e, = 0.78798 (from Eq. 2) using the values of C,, e,oo, ps and pf stated earlier. The implication of defining a different base for the depositional surface in the forward model is that the model curves from the Audet and McConnell (1992) model have to be shifted in depth so that the depth of 4, is consistent with that derived using Eq. (8). In the simulation runs for the Pathfinder Well, this shift is about 95.35 m (see Figure 6 (a)), which can be verified by evaluating Eq. (8) using e,, (T~= 10 kPa and the appropriate mechanical parameters. Using a constant sedimentation rate, the simulation was run for a dimensionless time of t = 140, which gave a final sediment thickness of about 5.4 km over a period of 5 Ma, assuming V, = 1400 m/Ma (see subsequent section). Results of forward modelling Figure 6 shows the results of using the forward model from Audet and McConnell (1992) to simulate the porosity and the excess pore pressure (JJ~-~,,,~,J of the Pathfinder Well. Using 5 < 1 < 10, it is possible to model the pore pressures in the upper, nearly normally pressured section (d < 2000 m) of the Pathfinder Well (Figure 6 (b)). The deeper, more highly overpressured section (d > 2000 m) can be modelled using 0.25 < I < 0.5. The associated porosity profiles (Figure 6 (a)) show that the porosity range at the bottom of the normally pressured section (1900 m) of the Pathfinder Well is consistent with the porosity data from the normally pressured section from Well SH #l . Figure 6 (a) also shows the theoretical compaction curve and the forward model curves for 1 = 0.25-10. At the top of the overpressured section (2200 m), the porosity of the Pathfinder Well is more consistent with I = 1 (in contrast to 0.25 < A < 0.5 for the excess pore pressure). This suggests that if the porosity data are accurate, then some secondary mechanism is contributing to the excess pore pressure below 2000 m in the Pathfinder Well, in keeping with the conclusions from Hart et al. (1995) and the theoretical results from Audet (1995b). The model from Audet and McConnell (1992) assumes a sedimentary column with homogeneous physical properties. The simulated results shown in Figure 6 clearly do not model the sharp pore pressure increase at d = 2000 m. However, this is not a serious limitation because of the following reasons. For the nearly normally pressured cases (1 = 5, lo), the pressure and porosity in the top 2 km of the column will be approximately the same, regardless of whether or not the underlying section
Marine and Petroleum
Geology 1996 Volume
13 Number 5 471
Compaction and over-pressuring
in Pleistocene
D. M. Audet
sediments:
IIISkempton (1944)
- HPathfinder Well
0.6
iP
??
[11 ‘\Well
SH #l
(Cc = 0.348) 1
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0
20
40
4
in Above
B Fault
X Below A Fault lithostatic
\\
80
100
Figure 7 The compression index (CJ as a function of the percent clay fraction. The clay fraction consists of particles with equivalent diameters less than 2 pm. The data (Skempton, 1944) shows that C, is proportional to clay content. The horizontal line shows the clay fraction range where the C, estimate for Well SH #I is likely to be found
(b) ~~~~~~‘ “~““~“~~~“ ~~~‘ ~ Pathfinder Well: \ ‘\,~Excess
60
% Clay fraction
(12.324
gradient:
MPa/km)
The effective permeability of Gulf Coast shales
0
10
30
20 Pf
-
40
50
Phydro
PW
Figure 6 Forward modelling of porosity (4) (a) and excess pore fluid pressure (or-ohvdro ) (b) for the Pathfinder Well. Part (a) shows the best fit of Eq. (8) (curve 6 from Figure 41, along with simulated porosity profiles for I = 0.25,0.5, I,5 and 10 (note the 95.35 m shift in the origin). Porosity data from the Pathfinder Well are shown at d = 1900 m (bottom of normally pressured section). Porosity section) and d= 2200 m (top of overpressured data from Well SH #I are shown for comparison. Part (b) shows the corresponding excess pore pressure profiles for 0.25 < d < 10. The excess lithostatic gradient (dashed line) is based on a reference lithostatic gradient of 22.621 MPalkm (1 psi/ft) and a hydrostatic gradient 10.297 MPa/km. Measurements for the Pathfinder Well are ;Prom Hart et al. (1995) taken above the B Fault and below the A Fault (see Figure 2b)
at d > 2 km is overpressured. Therefore, when modelling the top 2 km of the section, the variations in permeability at greater depth do not have to be taken into account in a first order model. Alternatively, when modelling the overpressured section at d > 2 km (1 = 0.25, 0.5, l), the excess pore pressure is controlled primarily by the permeability of the overpressured section and a detailed model of the more highly permeable overlying section is not needed. In principle, a more sophisticated model that takes into account changes in permeability due to lithology could be developed, but it is not strictly necessary for the results of this paper.
472
Marine and Petroleum
Geology 1996 Volume
The results of the forward model suggest a lower bound for the effective hydraulic conductivity of the Pathfinder Well sediments. In the Eugene Island area of the Gulf Coast, Pleistocene deposits (1.6 Ma) may be as much as 2.2 km thick (Galloway et al., 199I), suggesting an average sedimentation rate of about V, =2200/1.6= 1375 m/Ma, but this could vary by a factor of 5 or 10. Assuming I”’ = 1400 m/Ma, the effective hydraulic conductivity of the normally pressured sediments in the first 2000 m of the Pathfinder Well must be at least KO x 13 * lop9 cm/s, that is, using Eq. (11) with i = 5: -1 = 5*1,40OmMa-’ lOOcmm_’ ’ 3.15*10’3sMap’
2,70Okgm- _ 1 -’ 1,05Okgm-’
= 13 * l(pE. S
Likewise, in the overpressured section below 2000 m, the effective hydraulic conductivity can be no larger than ‘coz 2.6. 10d9 cm/s (using ;1 = 1). Therefore, regardless of the exact value of V. or the absolute value of ice, the transition from near hydrostatic pore pressures to high pore pressures at d = 2000 m of the Pathfinder Well can be explained by a reduction of hydraulic conductivity by a factor of 5. It is worth considering an alternative explanation for the pressure change at 2000 m in the Pathfinder Well. Instead of having a factor of 5 difference in the effective permeability, there could be a factor of 5 difference in the average sedimentation rate between the sediments above and below the fault splays in the Pathfinder Well. For purposes of illustration, consider first the case where the
13 Number 5
Compaction and overpressuring overpressured section (d > 2000 m) has been deposited at VO = 1400 m/Ma. By implication, in the shallower section the deposition rate must be 5 times lower, V, = 280 m/Ma, which means that it took at least 7.14 Ma to fill in the present-day section. Since the Pleistocene is about 1.6 Ma, there would not have been enough time for this scenario to take place. Alternatively, if the average sedimentation rate of the shallower section is V,, = 1400 m/Ma, then the rate in the deeper, overpressured section must be about V, = 7000 m/Ma, which is a very high number. According to figure 1 from Sadler (1981), most sediment accumulation rates are in the range 5 m/Ma < V, < 2000 m/Ma over 1 Ma time scales. Without biostratigraphic evidence from the Pathfinder Well, it would be hard to accept such a high value of V,,.In light of the available data, it is much easier to postulate a 5-fold change in permeability than a 5-fold change in average sedimentation rate. McCarthy (199 1) modelled the effective permeability of sand-shale mixtures by simulating fluid flow in a three dimensional composite material consisting of bodies of relatively impermeable material (i.e. shale inclusions) randomly embedded in a matrix of permeable material (i.e. sandstone matrix). The shale inclusions are spheroidal in shape with an anisotropy ratio 6 (ratio of major to minor axis). The numerical results were correlated using: k* = k,,(l -f)““,
(15)
where k,, is the sand permeability, f is the shale volume fraction, k* is the effective permeability of the sand-shale mixture and m is an exponent. McCarthy gave upper and lower bounds for m as a function of E. The upper and lower bounds account for the effects of the alignment of the spheroidal inclusions and differences between horizontal permeability (in the flow direction) and vertical permeability (perpendicular to the flow direction). Let kg and k;S be the effective permeabilities of the sediments in the normal and overpressured sections, respectively, and fNand f0 be the corresponding shale volume fractions. Using Eq. (15), consider the ratio of k$ to k::
(16) If the ratio k$/k,$ is specified, then for a given value offN the corresponding value of f. can be calculated. Rearranging Eq. (16) gives: fo=
;
1-(1-f,) 0
-Y
(17)
For example, assuming that k$/kg = 5, fN = 0.5 and m = 0.05, then f0 = 0.539 (see the first column of Table I). This example using the McCarthy model says that if the shale fraction in the normally pressured section is 50%, then the shale fraction in the overpressured section only has to increase by 3.9% (i.e. 53.9%) to decrease the effective permeability by a factor of 5. Table I shows f0 calculated using Eq. (17) for 0.4 < fN $ 0.6, a range consistent with results from DSDP Leg 96 (Stow et al., 1986). Depending on the exact value oft used, increasing fNby 0.03-0.20 can decrease kg by a factor of 5, which could account for the observed pore pressure change in the Pathfinder Well.
in Pleistocene sediments: D. M. Audet
Table 1 The shale fraction volume of the overpressured section Cfd required to give a permeability reduction kg/k+, = l/5 for a given shale fraction of the normally pressured section ( fN), based on the effective permeability model of McCarthy (1991). E is the anisotropy ratio of the spheroidal geometry used to model the shale inclusions. mlow and mop are lower and upper bounds for the exponent m in Eq. (15) (see table 2, McCarthy, 1991) f,forc=30 fN
mlow= 0.05
0.4 0.5 0.6
0.446 0.539 0.631
f,fort=lO m,,=0.13
0.513 0.594 0.675
m,0,=0.14 0.522 0.601 0.681
m,=0.25
0.599 0.666 0.732
If the effective permeability of the Gulf Coast sediments depends on the shale volume fraction, then the mechanical properties probably also depend on the shale content. Figure 8 shows the compression index, C,, as a function of clay fraction, defined as the percentage of sediment volume having an equivalent diameter less than 2 pm. In general, the compression index increases as the clay fraction increases. For C, = 0.348, the value for Well SH #l derived from log data, the sediment clay fraction could easily be between 20% and 45%. In the previous section, the same value of C’,was used to model both the shallower, normally pressured section and the deeper, overpressired section. This simplifying assumption is probably justified since the the scattered data in Figure 8 show that C, may not vary all that much with modest (1@30%) variations in clay (shale) fraction.
Discussion and conclusions Mud rich sediments in the Eugene Island area of the Louisiana Shelf show a normally pressured section about 2 km thick overlying an overpressured section. Using soil mechanics theory, the mechanical parameters (C, and el,,,) of the normally pressured sediments were estimated and found to be consistent with the results of consolidation tests made on Mississippi Fan sediments recovered during DSDP Leg 96, and with the general correlation for remoulded clays (Burland, 1990). The compaction curve based on the soil mechanics effective stress law is able to match the higher sediment porosities near the depositional surface, unlike the exponential law used by Hart et al. (1995). To fully appreciate how sediments compact at depth, it is useful to understand mechanical compaction in the early stages of burial. Since mechanical compaction is a major control on overpressure development, the effective stress must be modelled accurately, otherwise the onset of overpressuring can be mislocated by as much as 500 m, as shown for the case of Well SH #I. Using a one-dimensional compaction model (Audet and McConnell, 1992), porosities and pressure profiles for the Pathfinder Well were simulated. The excess pore pressures can be modelled provided that the sedimentation parameter is 0.25 < 1 < 1, suggesting that the effective permeability of the sediments in the overpressured zone is at least 5 times lower than that in the nearly normally pressured section (which can be modelled with 5 < /z < 10). The effective permeability model of McCarthy (1991) indicates that increasing the shale volume fraction by 3-20% could account for the decrease
Marine and Petroleum
Geology 1996 Volume
13 Number 5 473
Compaction and overpressuring
in Pleistocene sediments: 0. M. Audet
in permeability, suggesting that the top of the overpressured section is partially determined by stratigraphic factors related to the depositional environment of the sediments. The use of density and sonic logs, along with Issler’s (Issler, 1992) calibration curve, appears to provide a consistent framework for analysing effective stress, porosity and pore pressure in shale layers. Combined with soil mechanics theory, well log data can be used to better constrain mechanical compaction in forward basin models and to improve the understanding of excess pore pressure development.
Acknowledgements This work was supported by Amoco (UK) Exploration Company. The author thanks Peter Flemings and Bruce Hart for providing a preprint of Hart et al. (1995) and for useful comments on the manuscript.
References Atkinson, J. (1993) An introduction to the Mechanics ofSoils and Foundations, McGraw-Hill, London. Audet, D. M. (1995a) Modelling of porosity evolution and mechanical compaction of calcareous sediments Sedimenfology 42,355-373. Audet, D. M. (1995b3 Mathematical modelling of gravitational compaction and clay dehydration in thick sediment layers Geophys. J. Int. 122,283-298. Audet, D. M. and McConnell, J. D. C. (1992) Forward modelling of porosity and pore pressure evolution in sedimentary basins Basin Res. 4, 147-162. Bruce, C. H. (1984) Smectite Dehydration-its relation to structural development and hydrocarbon accumulation in northern Gulf of Mexico Basin AAPG Bulletin 68, 673-683. Bryant, W., Wetzel, A. and Sweet, W. (1986a) Geotechnical properties of intraslope basin sediments, Gulf of Mexico, De@o Sea Drillina Proiect Lea 96. Site 619. In: Init. Reefs. DSDP J. c. Coleman, A. W. Meier et al.) 96 (ids A. H. Biumi, Washington (U.S. Govt. Printing Office), 819-824. Bryant, W., Wetzel, A., Taylor, E. and Sweet, W. (1986b) Consolidation characteristics and permeability of Mississippi Fan sediments. In: /nit. Reefs. DSDP 96 (Eds A. H. Bouma. J. M. Coleman, A. W. Meyer’ef al.) Washington (U.S. Govt. Piinting Office), 797-809. Burland, J. B. (1990) On the compressibility and shear strength of natural clays Ggotechnique 40,329-378. Burst, J. F. (1969) Diagenesis of Gulf Coast clayey sediments and
its possible relation to petroleum migration AAPG Bulletin 53,73-93. Dickinson, G. (1953) Geological aspects of abnormal reservoir pressures in Gulf Coast Louisiana AAPG Sulletin37,410-432. Galloway, W. E., Bebout, D. G., Fisher, W. L., Dunlap, J. B. Jr, Cabrera-Castro, IX, Lugo-Rivera, J. E. and Scott, T. M. (1991) Cenozoic, In: The Gulf of Mexico Basin. (Ed. A. Salvador) Boulder, Colorado, Geological Society of America, The Geology of North America, v. J, 245-324. Hart, B. S., Flemings, P. B. and Deshpande, A. (1995) Porosity and pressure: role of compaction disequilibrium in the development of geopressures in a Gulf Coast Pleistocene basin Geology 23,45-48. Hower, J., Eslinger, E. V., Hower, M. E. and Perry, E. A. (1976) Mechanism of burial metamorphism of argillaceous sediment: I. Mineralogical and chemical evidence GSA Bulletin 87,725-737. Issler, D. R. (1992) A new approach to shale compaction and stratigraphic restoration, Beaufort-Mackenzie Basin and Mackenzie Corridor, Northern Canada AAPG Bulletin 76, 1170-1189. McCarthy, J. F. (1991) Analytical models of the effective permeability of sand-shale reservoirs Geophys. J. Inf. 105, 513527. Olsen, H. W. (1960) Hydraulic flow through saturated clays Clays ClayMineralsll, 131-161. Parasnis, D. S. (1960) The compaction of sediments and its bearing on some geophysical problems Geophys. J. Roy. Astron. Sot. 3, l-28. Perry, E. A. Jr and Hower, J. (1972) Late-stage dehydration in deeply buried pelitic sediments AAPG Bulletin 56,2013-2021. Rubey, W. W. and Hubbert, M. K. (1959) Role of fluid pressure in mechanics of overthrust faulting: II. overthrust belt in geosynclinal area of Western Wyoming in light of fluid-pressure hypothesis GSA Bulletin 70, 167-206. Sadler, P. M. (1981) Sediment accumulation rates and the completeness of stratigraphic sections J. Geol. 89, 569-584. Skempton, A. W. (1944) Notes on the compressibility of clays 0. J. geol. Sot. Lond. 100, 119-135. Stow, D. A. V., Cremer, M., Droz, L., Meyer, A. W., Normark, W. R., O’Connell, S., Pickering, K. T., Stelting, C. E., Angell, S. A. and Chaplin, C. (1986) Facies, composition and texture of Mississippi Fan sediments, Deep Sea Drilling Project Leg 96, Gulf of Mexico. In: /nit. Repts. DSDP 96 (Eds A. H. Bouma, J. M. Coleman, A. W. Meyer et al.) Washington (U.S. Govt. Printing Office), 475-487. Terzaghi, K. (1927) Principles of final soil classification Public Roads8,41. Terzaghi, K. (1936) The shearing resistance of saturated soil and the angle between the planes of shear. In: froc. of Ist International S/WE Conference. Harvard, Mass. 1, 54-56. Wangen, M. (1992) Pressure and temperature evolution in sedimentary basins Geophys. J. Int. 110,601-613. Wetzel, A. (1989) Influence of heat flow on ooze/chalk cementation: quantification from consolidation parameters in DSDP Sites 504 and 505 sediments J. Sediment. Petrol. 59,539-547.
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