Well-log analysis of pore pressure mechanisms near a minibasin-bounding growthfault at South Eugene Island field, offshore Louisiana

Matthew M. Haney1, Ronny Hofmann2 , and Roel Snieder11Center for Wave Phenomena, Department of Geophysics, Colorado School of Mines, Golden, CO 804012Center for Rock Abuse, Department of Geophysics, Colorado School of Mines, Golden, CO 80401now at: Sandia National Laboratories, Geophysical Technology Department, Albuquerque, NM 87185

Summary

Using well log data from the South Eugene Island field,offshore Louisiana, we derive empirical relationships be-tween elastic parameters (e.g., P -wave velocity, density)and effective stress along both normal compaction andunloading paths. These empirical relationships providea physical basis for numerical modeling and allow us toinvestigate the effect of fluid pressure. The presence ofmore than one stress path complicates the prediction offluid pressure from seismically derived interval velocitiessince the relationship between seismic velocity and porepressure is multi-valued.

Introduction

Empirical relationships between pore pressure and threebasic rock properties - porosity, density, and sonic velocity- are necessary for numerical modeling of the interactionof fluids and seismic wave propagation. The fact that porepressure largely controls rock matrix properties in com-pacting sedimentary basins allows methods for imagingseismic reflections to indirectly measure spatially varyingpore pressure distributions. In order to facilitate physi-cally meaningful numerical modeling of fault-plane reflec-tions arising from fluid pressure distributions, we haveexamined well logs for indications of pore pressure in ex-cess of hydrostatic, or overpressures. The data for thisanalysis come from wells drilled at the South Eugene Is-land field, offshore Louisiana. The variation of the threerock properties with effective stress reveals a hystereticbehavior that occurs during the compaction of sediments.Evidence for both plastic (irreversible) and elastic (re-versible) deformation exists in the available well data andpressure tests. These two regimes point to different un-derlying causes of overpressure (Hart, 1995). For thesedual deformation mechanisms, we construct two empir-ical relationships between each rock property and porepressure - one valid for each regime.

Porosity versus depth

Compaction acts to reduce the porosity of sediments asthey are buried; however, this process can continue onlyas long as fluids in the diminishing pore space are al-lowed to be expelled. Such would be the case in normally

FB

A

Hydrostatic

N

100 m

Z

A20ST

Overpressured

Fig. 1: Cartoon depth section (bottom) of the subsurface at SouthEugene Island. The four main growth faults are shown in the bot-tom panel as the A, B, F, and Z faults. Throw across the faultsis depicted by the layer running from left to right. Most of thewells at South Eugene Island were drilled into the shallow, hydro-static section; the A20ST well was unusual in that it was continuedthrough the A-fault system and into the deep overpressured com-partment.

pressured, hydrostatic sediments in which the fluids arein communication up to the seafloor. Once the move-ment of the fluids out of the pore space is opposed, asin a compartment sealed-off by low permeability or highcapillary-entry-pressure shales or fault gouge, the poros-ity remains constant with burial depth if the fluid is moreor less incompressible. This situation is called undercom-paction (Huffman, 2002). Undercompaction means thesediments are frozen in time and are simply buried intheir unchanging earlier compaction state (Bowers, 1995).To compound the situation, if fluid from outside the un-dercompacted sediments is pumped into the pore space,or if hydrocarbons are generated from within the under-compacted sediments, a process called unloading occurs.Whereas undercompaction can only cease the reductionof porosity, unloading can actually reverse the trend andincrease porosity. Although unloading can reverse thetrend, it cannot reclaim all of the previously lost porosity.This is because the compaction process has a large irre-versible component. In contrast, unloading and loading ofsediments by pumping fluid into and then depressurizingthe pore space is a reversible process, insofar as the fluiddoes not cause hydrofracturing.

We have studied wireline data taken in wells at the SouthEugene Island field, offshore Louisiana, for indicators ofoverpressure, such as constant porosity as a function of

Overpressure mechanisms near a fault

0 1000 2000 30000

0.1

0.2

0.3

0.4

0.5

depth (m)

poro

sity

1 2

Fig. 2: Porosity versus depth at South Eugene Island. The thick,solid line is the best-fit normal compaction trend using Athys Law.The faint solid lines are density-derived porosity values from 11wells at South Eugene Island. To obtain the porosity, we assumethat the solid grains have a density of 2650 kg/m3 and the fluid hasa density of 1000 kg/m3 , as in Revil and Cathles (2002). There isa clear break from the shallow, exponentially decreasing porositytrend at a depth of 1800 m, at which point the porosity remainsconstant with increasing depth, as shown by the flat dashed line.The two circles are density-derived porosities from the upthrownblock to the north of the minibasin at South Eugene Island. Thedashed lines connecting the circles to the main compaction trendare the interpreted porosity histories of the samples. They show aperiod of undercompaction, depicted as a horizontal line deviatingfrom the normal compaction trend, followed by a vertical unloadingpath due to a late-stage pore-pressure increase.

depth. Previous work by Hart et al. (1995) shows thecrossover from hydrostatic to overpressured conditions inporosities derived from sonic velocities. Here, we take aslightly different, perhaps more straightforward approachbased on the density log. The South Eugene Island fieldis a Plio-Pleistocene minibasin formed by salt withdrawaland has yielded more than 300 million barrels of oil in itslifetime. A cartoon depiction of the subsurface at SouthEugene Island is displayed in Fig. 1. The main part ofthe field is a vertical stack of interbedded sand and shalelayers bounded by two large growth faults to the northand south.

Fig. 2 shows porosity derived from density logs taken inthe following wells at South Eugene Island: A13, A20ST,A14OH, A15, A23, A6, B10, B1, B2, B7, and B8. Becausethe geology in the minibasin is essentially horizontally lay-ered, we ignore the fact that some wells may be miles awayfrom each other and simply look at the depth variationof their porosity. In all the well logs shown in this paper,we have done some smoothing with depth (over 100m) to remove any short-range lithologic influences (e.g.,sand versus shale) on the density and velocity. To obtainthe porosity from the density log, we take the solid grainsto have a density of 2650 kg/m3 and the fluid to have adensity of 1000 kg/m3, as in Revil and Cathles (2002).There is a clear break from the shallow, decreasing poros-

ity trend at a depth of 1800 m. We take this depth as theonset of overpressures in the sedimentary section, beneatha shale bed located above a layer called the JD-sand. Byfitting an exponential trend to the porosity values above1800 m, we get the normal compaction trend in the hy-drostatically pressured sediments

c(z) = 0.47 e0.00046 z, (1)

where, in this equation, the depth z is in meters. Thesuperscript c in equation (1) refers to the fact that thisfunctional relationship characterizes normal compaction.In the porosity-versus-depth plot of Fig. 2, this relation-ship holds for any movement toward the right on the nor-mal compaction curve and any purely right-going hori-zontal deviations from the normal compaction curve. Forpurely right-going horizontal deviations, the depth z usedin equation (1) is equal to the depth at which the horizon-tal deviation started. The two circles in Fig. 2, representsamples taken in the A20ST well and are connected tothe normal compaction curve by both horizontal and ver-tical lines. The vertical lines show the departure of thesamples from the normal compaction trend. We return tothese in the next section. Note that the sediments deeperthan 1800 m in Fig. 2 maintain a nearly constant poros-ity of around 0.2 during subsequent burial (a horizontaldeviation from the compaction trend).

Density versus vertical effective stress

Since bulk density, and not porosity, is a more widely usedparameter in simulations of seismic wave propagation, wehave studied the variation of bulk density with fluid pres-sure. By looking at bulk density, we also leave the originaldata, a density log, unaltered by assuming certain solidand fluid densities. In contrast to the preceding section,we want to see how density changes with effective stress,instead of depth. To accomplish this, we take only themeasurements that are shallower than 1800 m, where thepore pressure is, by all indications, hydrostatic. There-fore we know the pore pressure and can calculate the ef-fective stress. In overpressured compartments, since thepore pressure is unknown, direct measurements by Re-peat Formation Tests (RFTs) are necessary to calculatethe effective stress.

We rewrite equation (1) in terms of density and effectivestress using the relationships

= s(1 ) + f , (2)

andd = fgz, (3)

where is the bulk density and s and f are the densitiesof the solid and fluid components. Note that the relation-ship for d holds only under hydrostatic conditions. Fromthese relationships and equation (1), we obtain the nor-mal compaction curve for density

c(d) = s 0.47 (s f ) e0.0003d , (4)

Overpressure mechanisms near a fault

0 1000 2000 3000 40001800

2000

2200

2400

v P (psi)

dens

ity (k

g/m3 )

1

1 2

2

Fig. 3: Density versus effective stress at South Eugene Island. Thethick solid line is the same normal compaction trend shown in Fig.2, except transformed into density and effective stress. The faintsolid lines are also the same as in Fig. 2, except that they are nowlimited to the hydrostatic depths down to 1800 m. The circlesrepresent two pressure measurements, labeled 1 and 2, which weremade in the overpressured upthrown block where a density log alsoexisted. For each pressure measurement, we plot the data pointtwice - one where it should lie on the normal compaction curvewere it to have been normally pressured, and the other where itactually does plot because of severe overpressure. Note that sample1 is from a greater depth than sample 2.

where s and f are the densities of the solid and fluidcomponents, taken as 2650 kg/m3 and 1000 kg/m3 respec-tively, and d is in psi. We plot this normal compactioncurve in Fig. 3 together with the density measurements.Also, in Fig. 3, we show as circles two data points ob-tained from RFT pressure measurements and density logmeasurements in the overpressured upthrown block. Weshow the circles in two locations - one on the normal com-paction trend where they would plot if the measurementswere at hydrostatically pressured locations, and the otherwhere they actually plot because of severe overpressuresbeing present in the upthrown block.

At this point, we dont know exactly how the samplestaken in the upthrown block came to be off the normalcompaction trend. Using a laboratory measurement of theunloading coefficient by Elliott (1999) on a core sampletaken near the locations of samples 1 and 2, the paththat these samples took to their present locations can beestimated. Elliott (1999) characterized the unloading, orelastic swelling, for the porosity of the core samples to be

u(d) = 0 (1 d) , (5)

where 0 and characterize the deviation of the unload-ing path from the normal compaction trend. Note thesuperscript u, in contrast to equation (1), indicating theunloading path instead of the normal compaction trend.Elliott (1999) found that 0 = 0.37 and = 0.98 10

8

Pa1 for the unloading path. Though these parametersdescribe the porosity, we use them to find the slope ofthe unloading path for density using the relationships be-tween porosity and density described earlier. After find-ing this slope, we can construct the unloading path for

the density from equation (4) and the slope

u(d) = 0.04 (d max) + s

0.47 (s f ) e0.0003max . (6)

This expression contains an extra parameter max thatrefers to the value of the effective stress when the samplebegan to be unloaded. We do not know max for samples1 and 2, but we do know that max must lie on the maincompaction trend. Hence, we can construct linear unload-ing paths for the density, as shown by the dashed lines inFigure 3. With these unloading paths, we can then findthe value for the maximum past effective stress max. It isworth mentioning that the maximum past effective stressfor sample 1 comes out to be 1500 psi by our approachof using Elliotts experimental results. In an independentmeasurement, Stump and Flemings (2002) performed uni-axial strain tests on a core sample taken from the samelocation as sample 1 to find the maximum past effectivestress. Stump and Flemings (2002) report a value of 1248psi for this sample, close to our estimate of 1500 psi;visually, the discrepancy lies within the error bars of thenormal compaction curves fit to the density log data.

With the estimate of the maximum past effective stress,we can also return to Fig. 2 and find the depth at whichsamples 1 and 2 left the normal compaction trend, sincein the hydrostatic zone the depth is a linearly scaled ver-sion of the effective stress. These depths correspond to aslightly lower porosity than that of samples 1 and 2. Weinterpret this as being the result of a late stage porosityincrease and represent it as a vertical unloading path forsamples 1 and 2 in Fig. 2.

Sonic velocity versus vertical effective stress

For the purposes of modeling faults and to make infer-ences about the distribution of pore pressure from seis-mic interval velocity inversions, accurate pore-pressure-versus-velocity relationships are critical. In general, sonicvelocity has a normal compaction curve and unloadingpaths as a function of effective stress that are similar tothose we just described for the density well log data. Toobtain these relationships, we proceed as for the densitylogs: 1) We take 12 shallow wells to make up a data setof sonic velocity versus effective stress. 2) We select thedepth range with hydrostatic pressures and plot the sonicvelocity versus effective stress. 3) We fit this with a powerlaw relation for the normal compaction trend. 4) We thenlook at where the two samples from the overpressuredupthrown block lie and construct unloading curves usingthe estimate for the maximum past effective stress thatwe obtained in the previous section on density. The wellswe use for characterizing the sonic velocity come fromA20ST, A14OH, A23, A6, B10, B1, B2, B7, B8, A1, B14,and B20.

In Fig. 4, we plot the normal compaction trend for sonicvelocity as a thick solid line described by the power law

Overpressure mechanisms near a fault

0 1000 2000 3000 40001500

2000

2500

3000

v P (psi)

son

ic v

eloc

ity (m

/s)

2

1

1 2

Fig. 4: Sonic velocity versus effective stress at South Eugene Is-land. The thick solid line represents the normal compaction curvefitted to the shallow well data, shown in the faint solid lines. Wealso plot samples 1 and 2 both where they should fall on the normalcompaction trend, were they to be normally pressured, and wherethey actually plot due to the severe overpressure where they wereobtained. Using the estimate for past maximum effective stressfrom the density plot and the Bowers-type relation (Bowers, 1995)shown in equation (8), we are able to construct the velocity un-loading curves, shown as dashed lines.

equation (Bowers, 1995)

vcp(d) = 1500 + 2.3 0.77d , (7)

where the P -velocity is in m/s and differential pressureis in psi. Note again the superscript for the normal com-paction relation. We also construct the unloading curvefor vp following the relationship first suggested by Bowers(1995)

vup (d) = 1500 + 2.3

"max

d

max

1/6.2#0.77, (8)

where d and max are in psi and vp is again in m/s.

To model elastic waves, one other parameter is needed inaddition to and vp; for instance, a seismologist wouldnaturally want the shear velocity. In the absence of infor-mation on the shear wave velocity vs and pressure in theshallow, hydrostatic sediments, we assume that

vs(d) = vp(d) 1500, (9)

where this relationship holds on both the normal com-paction curve and the unloading path. The data pre-sented by Zimmer et al. (2002) for unconsolidated sandssupports this assumption, in that the dependence theyfound for vs on effective stress is essentially a down-shiftedversion of the vp curve. An additional piece of supportingevidence comes from the only vs data available at SouthEugene Island, a shear log from the A20ST well, wheresamples 1 and 2 were taken. There, the ratio of vp/vsfrom the sonic and shear logs falls between 3 to 3.5 in theoverpressured upthrown block.

Conclusion

We have established two empirical relationships betweeneach of three basic rock properties and pore pressure atthe South Eugene Island field. Most important for sub-sequent numerical modeling of seismic wave propagation,we have found relationships for the density and the sonicvelocity vp on both the normal compaction and unload-ing paths. We plan to use the empirical relationshipsbetween the elastic parameters and fluid pressure to sim-ulate fault-plane reflections from different pressure distri-butions around fault zones.

Acknowledgments

We thank Shell International Exploration and Productionfor access to the well log data and to Jon Sheiman forhelpful discussions on pore pressure.

References

Bowers, G. L., 1995, Pore Pressure Estimation fromVelocity Data: Accounting for Overpressure Mech-anisms Besides Undercompaction: SPE Drilling &Completion, June, 89-95.

Elliott, D. A., 1999, Hydrofracture Permeability Re-sponse and Maximum Previous Consolidation StressEstimations for Faulted and Micro-Faulted Silty-Shales Taken from the Eugene Island Block 330 FieldPathfinder Well in the Gulf of Mexico. MSc Thesis,University of California, San Diego.

Hart, B. S., Flemings, P. B., and Deshpande, A., 1995,Porosity and pressure: Role of compaction disequi-librium in the development of geopressures in a GulfCoast Pleistocene basin: Geology, 23, 45-48.

Huffman, A. R., 2002, The future of pore-pressure pre-diction using geophysical methods: The LeadingEdge, 21, 199.

Revil, A. and Cathles III, L. M., 2002, Fluid transport bysolitary waves along growing faults: A field examplefrom the South Eugene Island Basin, Gulf of Mexico:Earth and Planetary Science Letters, 202, 321-335.

Stump, B. B. and Flemings, P. B., 2002, Consolida-tion State, Permeability, and Stress Ratio as Deter-mined from Uniaxial Strain Experiments on Mud-stone Samples from the Eugene Island 330 Area, Off-shore Louisiana in: Pressure regimes in sedimentarybasins and their prediction, eds. A. Huffman and G.Bowers, AAPG Memoir 76.

Zimmer, M., Prasad, M., and Mavko, G., 2002, Pressureand porosity influences on VP VS ratio in uncon-solidated sands: The Leading Edge, 21, 178-183.