Physical properties of shallow-water flow (SWF) sands dif-fer from most reservoir and seal rocks studied for petro-leum purposes. These materials exist near the transitionzone between rocks and sediments. Our investigations, thesubject of this article, suggest that physical properties ofSWF sands are amenable to a prediction methodology thatuses high-resolution multicomponent seismic data.

SWF sands are a primary hazard to deepwater drillingoperations in the Gulf of Mexico. They have the potentialto result in well failures and significant discharges of sub-surface fluids into the ocean. However, at present, mostoperators make only a modest attempt to identify SWFbefore drilling. They drill through these hazards and mit-igate any resulting damage at significant expense if one isencountered. This is not rare. According to a report fromFugro Geoservices, approximately 70% of all deepwaterwells have experienced SWF.

Amethod for predrill delineation of sands that are closeto failure, and thus likely to exhibit SWF, would be advan-tageous in selecting optimal drilling locations and in devel-oping cost-effective well plans. The current method ofidentifying SWF involves predrill hazard studies utilizingconventional and high-resolution seismic data to identifyzones that might produce SWF. However, the high incidenceof SWF mitigation events in deepwater wells shows thatexisting techniques do not provide adequate resolution oraccuracy.

At present, no robust seismic method exists for accu-rately identifying and characterizing SWF. Operators do nothave the option to avoid the hazard instead of mitigatingthe problem after it has started. A new method is requiredthat will permit operators to identify the hazard before thewell is drilled.

Using seismic data for accurate understanding of thephysical properties and deformational behavior of SWFsands is essential to characterization, prediction, and inter-pretation of these stratigraphic units. To date, very fewcore and log formation evaluation measurements have beentaken in these shallow intervals because they are not of eco-nomic interest.

Physical conditions of SWF formations. SWF sands havebeen observed in water depths 1500-7000 ft beneath theseabed and 4000 ft below the mud line. At these depths ofburial, materials are virtually unconsolidated and havevery high porosities and very low effective stresses. Therange of confining and effective stresses for these sands canbe estimated from first principles to be, respectively, 700-6500 psi and 0-1000 psi. To put this in perspective, it is valu-able to compare stress conditions in a shallow-water anda deepwater case (Figure 1). In both, effective stress on theformation at the mud line is zero. It increases with a gra-dient of about 0.535psi/ft if hydrologic communication ismaintained with the ocean water column. In shallow water,effective stress becomes nonzero 500 ft below sea levelwhere the total overburden stress is relatively small. At awater depth of 4000 ft, however, overburden stress is muchlarger due to the higher water column. However, as long

as pore fluids are in pressure communication, pore pres-sure will increase an equal amount. Thus, effective stressremains unchanged between shallow and deepwater at thesame depth below mud line. In this example case, it is pos-sible that an SWF zone could be 6000 ft below mean sealevel and 2000 ft below mud line and exist at a confiningstress of 3100 psi and an effective stress of about 1100 psi.This compares to a shallow-water case (water depth of 500

1030 THE LEADING EDGE SEPTEMBER 2001 SEPTEMBER 2001 THE LEADING EDGE 0000

The petrophysical basis for shallow-water flowprediction using multicomponent seismic data

ALAN R. HUFFMAN, Conoco, Houston, Texas, U.S.JOHN P. CASTAGNA, University of Oklahoma, Norman, U.S.

Figure 1. Examples of confining stress (dashed curves)and effective stress (solid curves) from shallow water(blue curves) and deep water (red curves) showing thecontrast in loading conditions. Note that the differencebetween the red curves at depths of 4000 and 7000 ft,which represents the pore pressure, is much larger thanthe difference between the blue curves at the samedepth.

Figure 2. Model of sand deposited on a flat surfaceand then positioned structurally to create a hyperpres-sured reservoir. At time 1, the sand is in equilibriumwith all pressures equal. At time 2, sand pressures aredifferent with respect to each other and with respect tothe pressures in the adjacent shales and are affected bythe type of structure. (From Stump et al.)

ft) in which the confining stress is 4750 psi and the effec-tive stress is 3100 psi. The pore pressures that equate to thesetwo cases are 2000 psi for deep water and 1650 psi for shal-low water, or a difference of 350 psi at the same depth rel-ative to sea level. Thus, not only are sediments in thedeepwater case less compacted, but they are at relativelyhigher pore pressures for the same depth below sea level.

In addition to the change in compaction state for deep-water sediments, the severity of SWF may be exacerbatedby the presence of structural hyperpressuring, also knownas the centroid effect (Traugott and Heppard, 1994). Theconcept of structural hyperpressuring suggests that a sandbody on a structure or slope will develop a pressure gra-dient that is hydrostatic, even though the gradient in thesurrounding sediments is nonhydrostatic (Figures 2 and 3).This effect produces a condition in which the updip limbof a sand body with large areal extent may have much

higher pore pressures than the surrounding shales (theycan even approach the fracture gradient). The character ofthe structure (e.g., synclinal versus anticlinal) also deter-mines the reservoir pressure to some extent (Figure 3). Forthe shallow burial conditions in which SWF occur, theamount of structural hyperpressuring required to cause aseal failure is not large. Hence, it is easy to picture a situa-tion (Figure 4) in which a sand is deposited on the slopewith a large downdip extent and then buried under a finiteamount of overburden, producing a structurally hyper-pressured reservoir that will result in SWF when pene-trated.

Petrophysical properties. To understand the petrophysi-cal properties of SWF sands, one must consider their depo-sition and burial. Sands and shales are deposited on theseabed in a form that resembles a slurry more than a rock.Smith (1974) characterized the behavior of these fine- andcoarse-grained sediments using Wood’s equation for sus-pensions (Figure 5). As materials are buried, they begin todeviate from the Wood’s equation and become load-bear-

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Figure 3. Pressure diagram showing relationshipbetween structurally hyperpressured sand in Figure 2and the surrounding shales. Numbers correspond tonumbers defining structural position of each sand inFigure 2. Numbers 4, 6, and 8 represent pressure at thetop of the sand body. Numbers 5, 7, and 9 representpressures at the bottom of the sand. Numbers 2 and 3are pressures at the top and bottom of the shale. Thecentroid of each sand is the point at which reservoirpressure intersects shale pressure. (From Stump et al.)

Figure 4. Types of shallow-flowing sands characterizedby their hydrologic continuity and ability to produce agiven volume of fluid. Note the large volume of waterthat can be produced by sands that have large downdipextents and structural hyperpressuring (red) versusthose with small extent (yellow).

Figure 5. Porosity velocity relationships observed inmarine sediments. Differences between the measure-ments and the curves for Wood’s equation are probablydue to development of frame rigidity. (After Smith.)

Figure 6. Pulse transmission measurements on brine-saturated sand packs. Open circles are our data whichare fit by a power-law empirical relation, as described inthe text (solid line). Open squares are measurementsfrom Prasad.

ing materials with a granular frame that develops rigidity.The porosity point at which sediments begin to behave likeload-bearing framework solids was termed the “criticalporosity” by Amos Nur. This change in behavior is animportant transition because it signals the point at whicheffective stress becomes nonzero. As effective stressincreases, compaction causes porosity to decrease and thematerial becomes more rocklike in its behavior. However,the slower rate of increase in effective stress in deepwaterconditions also causes the rate of compaction to decrease,causing these materials to have a relatively higher poros-ity than a shallow-water material at the same depth belowsea level.

Evaluation of the physical properties pertinent forpredrill seismic characterization of SWF must include com-pressional and shear velocities, attenuation and densitiesof the materials, and the strength of the sand frameworkunder dynamic loading. Basic understanding of these prop-erties can be estimated from first principles of compactiontheory for sediments and soils, and from the literature onvelocity-effective stress relationships in clastic sediments.If we consider the range of confining and effective stressesunder which SWF sands exist, it is recognized that thesematerials exist in the transition zone between Wood’s equa-tion behavior for slurries and porous load-bearing granu-lar materials that can be modeled using Biot theory. Atthese conditions, the formation should show modestchanges in compressional velocity with the observed pore-pressure changes. In contrast, small changes in pore pres-sure will cause large changes in shear-wave velocity as thematerial moves very close to the critical porosity whichresults in the rigidity, or shear strength, of the materialrapidly approaching zero. The combination of these twopredictions suggests that the VP/VS ratio of these sandsmay change dramatically under small load changes (Figure6). The equations of Castagna et al. (1993) suggest thatbelow a certain effective stress, there is a rapid increase inthe VP/VS ratio (which is directly related to Poisson’s ratio).It is reasonable to assume that this is accompanied by a rapidincrease in shear-wave attenuation with very smalldecreases in effective stress. This occurs because rock rigid-ity is approaching zero (i.e., the sediment is becoming morelike a liquid). At higher effective stresses, the rock frame ismore rigid and the sediment behaves more like a solid. Theregion of rapid rigidity loss is a likely candidate for SWF.The loss of rigidity may also be tied back to the strength ofthe materials and their resistance to liquefaction and for-mation collapse. Poisson’s ratio, the modulus of rigidity,and shear-wave quality factor (Q or attenuation) should behighly anomalous for sands close to failure and prone toSWF.

To confirm the above postulates, measurements of com-pressional- and shear-wave velocities were performedunder a range of confining and pore pressure conditionsappropriate for SWF problems—porosities of 32-50%, 0-8%shale, and a range of frequencies using conventional ultra-sonic pulse transmission techniques. These measurementswere performed at the IC3 facility (the former BP Amocorock-physics lab known as the Integrated CoreCharacterization Center) at the University of Oklahoma inTulsa. The data set was completed by measuring the dryvelocities on a sand pack and then backfilling with brineto measure water-saturated properties. Effective stress var-ied from 3750 psi to 200 psi in dry samples and down to400 psi in saturated samples. Shear-wave measurementswere stopped at these two stresses, respectively, due to lossof coupling of the transducers to the sample and/or

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Figure 7. Pulse transmission water-saturated VP (opencircles) and VS (open squares) measurements from thisstudy, including the data of Bell (1979) and Domenico(1977). Solid lines are power-law fits to the VP and VSdata, as described in the text.

Figure 8. VP/VS ratio plotted against effective pressureon a logarithmic scale for pressures between 10 and 10 000 psi and VP/VS less than 8. Open circles are mea-surements from this study on clean brine-saturatedsands, and open squares are measurements by Prasad.Solid line is predicted VP/VS from power-law fit to ourmeasurements. Solid red line is Prasad’s reportedempirical fit.

Figure 9. VP/VS plotted against effective stress for brine-saturated sand packs containing 8% clay by weight(open circles) and power-law empirical fit. Brown line isthe clean sand trend from Figure 8. Red line is Prasad’sreported trend.

increased shear-wave attenuation; either resulted in inabil-ity to detect the transmitted shear wave.

Figure 7 shows a compilation water-saturated VP andVS measurements from this study, with the data of Bell(1979) and Domenico (1977) added. The velocities are read-ily fit by power-law equations of the form

V = a + b Pc

where P is the effective pressure. The constant a is con-strained by Wood’s equation at zero effective stress for P-wave velocities and is taken to be zero for shear-wavevelocities in clean sands. The empirical coefficients b andc are then obtained by curve fitting the data. We find forthe clean sands in Figure 7 (velocity is m/s and pressurein bars)

VP: a = 1700, b = 200, c = .22VS: a = 0, b = 270, c = .26

It is obvious by inspection of Figure 7 that the data can onlybe approximately fit by equations of this form because thecoefficients will vary with porosity and composition.However, when taking the ratio of VP to VS, the scatter ismuch reduced (Figure 8) and a remarkably good fit results.The data of Prasad (in press and also shown in Figure 8)are in general agreement with the VP/VS trend but higher

VP/VS ratios (we suspect this is due to higher porosities inPrasad’s samples). Clearly, the spread in the data suggeststhat additional calibration of VP/VS trends will be needed.

We find a similar a power-law pressure dependence forsand packs that have 8% clay by weight. For these clay-rich sand packs, we find

VP: a = 1640, b = 180, c = .26VS: a = 160, b = 210, c = .30

The resulting VP/VS trend (Figure 9) exhibits lower VP/VSthan the clean sand trend from this study and Prasad’strend. These low VP/VS ratios may indicate that smallamounts of clay act to bind the loose sand grains, therebydecreasing VP/VS at a given pressure.

Models for SWF seismic response. The laboratory mea-surements of compressional- and shear-wave velocitiesassociated with pressure changes in the sands were usedto generate a series of seismic model responses. Modelscomprised multiple layers of shale with montonicallyincreasing velocity and density and with an imbeddedsand layer representing the SWF reservoir unit.

The model results suggest that the large changes pre-dicted in VS and VP/VS ratio will result in significant changesin the AVO response of the SWF sand units. The P-wavegathers (Figure 10) show a modest change in reflectivityand a significant change in the reservoir’s AVO responseas a function of effective stress. Likewise, the mode-con-verted S-wave gathers, or PS events (Figure 11), show a dra-matic change in reflectivity and a change in polarity as afunction of effective stress. The PS reflection gathers alsoshow significant attenuation on the low effective stressmodels not present on the higher effective stress models.Furthermore, the large changes in attenuation exhibited bythese sands will also cause significant frequency loss on seis-mic data. The seismic responses from these models indi-cate that high-resolution AVO and inversion methodsshould be able to resolve the changes in pressure and fail-ure state that are related to the SWF problem. Analysis ofthe attenuation properties also suggests that changes inattenuation should be observed below sands that are abnor-mally pressured and prone to SWF, as evidenced by the lossof reflectivity at low effective stresses in Figure 11. It is alsohighly likely that given multicomponent seismic data,Poisson’s ratio, modulus of rigidity, and shear-wave qual-ity factor can be extracted with greater resolution and accu-racy than from conventional seismic data. Attenuationshould be detectable, particularly on multicomponent data,by analyzing the P-wave reflections from the SWF zone andmode-converted shear-wave reflections from SWF intervalsand below them. Attenuation of both P- and S-reflectionsthat have traveled through the SWF zone should be sig-nificant and should allow these zones to be mapped.

To determine whether real multicomponent data canresolve changes in physical properties associated with SWFconditions, we worked in conjunction with PGS Reservoirto evaluate the value of these data for shallow hazard analy-sis. Various sites were selected from the Gulf of Mexico(GOM), where PGS has acquired 2-D multicomponentocean-bottom cable data (OBC). A proprietary multicom-ponent VP/VS inversion method was applied to these data.Results suggest that the variations in velocity and imped-ance resulting from SWF sand bodies will be detectable onseismic data (Figure 12). In particular, it appears that mode-converted shear-wave data are particularly useful in obtain-ing a high-resolution estimate of VP/VS.

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Figure 11. Seismic gathers for mode-converted S-wavereflection (PS) events from model showing change inreflectivity with effective stress. Left model is a refer-ence shale layer. Models 2-6 represent decreasingeffective stress from 3750 psi down to 100 psi. Notelarge change in polarity and reflection strengthbetween gathers 4 and 6.

Figure 10. Seismic gathers for P-wave reflection eventsfrom model showing change in reflectivity with effec-tive stress. Left model is a reference shale layer.Models 2-6 represent decreasing effective stress from3750 psi down to 100 psi.

We also investigated the use of conventional AVO analy-sis of shallow reflections. Such analysis is problematic forOBC data because the unusual geometry is not well suitedfor AVO analysis of shallow events. However, conventionalAVO analysis was performed to see if anomalous behav-ior could be observed empirically. Figure 13 shows anapparent high Poisson’s ratio anomaly in the vicinity of awell exhibiting a shallow-water flow.

Mechanical failure. At very low effective stresses, physi-cal conditions in these SWF sands are such that they areclose to critical porosity with porosities from 38% to 50%,depending on the sorting and shaliness of the specific strati-graphic unit. The high porosities and uncemented, uncon-solidated nature of these sands plus the very low effectivestresses also suggest that they should have very low fail-ure strengths and may exist in a state of incipient failurethat allows them to flow into a well bore when penetratedby the drill bit. SWF sands often are abnormally pressuredup to 200 psi above the surrounding sediments, which mayincrease the mechanical instability that leads to significantflows. In a relative sense, the actual pore pressure differ-ence in these sands is very small, often less than 100 psi.However, such small changes in pressure at these shallowdepths of burial can lead to significant water flows that cancause formation collapse and massive sanding into a well.The unconsolidated state of these sediments also providessufficient formation porosity such that the volume of pro-ducible water can be quite large. When an SWF sand hasan extensive downdip extent, the volume of produciblewater and the hydrostatic support available to maintain theflow for long periods of time can be severe.

A major question regarding SWF is the cause of failure.At present, there are two likely possibilities.

First, it is possible that these materials are already in anincipient state of failure and that drilling simply initiatesthe flow by dynamic loading of the sediments at the well-bore interface. The analog for this type of failure is wellknown in earthquake literature and is called liquefaction.Liquefiable materials documented from earthquake stud-ies (Richart et al., 1970) tend to be high porosity and of acoarse granular nature, very similar to SWF sands. Thesefailures are caused by the rearrangement of grains due todynamic loading that causes the local pore pressure toincrease dramatically as the material attempts to compactunder the loading. Such materials have been documentedto flow to the surface and vent spectacularly, as has beenobserved in some SWF case studies.

Second, it is possible that these materials are so cohe-sionless that the mere flow of formation water into the wellbore causes the sand to flow as well, and that the sustainedflow of formation water eventually destabilizes the entire

formation and results in a total collapse of the SWF inter-val. Effectively, this is a type of catastrophic sanding prob-lem.

The difference between these two failure modes is sig-nificant. Catastrophic sanding can likely be mitigated bychanges in drilling fluid pressure and properties but liq-uefaction must be mitigated by decreasing the dynamicloading induced by the drilling operation so that the for-mation does not “feel” the drill bit passing through it. Moredirect measurements of SWF zones while drilling areneeded to determine which failure mode is occurring. It ispossible that both failure modes are present, but the dataavailable to date are insufficient to distinguish betweenthem.

Conclusions. Physical properties of SWF sands differ frommost reservoir and seal rocks studied for petroleum pur-poses. These materials exist near the transition betweenrocks and sediments, and the results of this study suggestthat the physical properties of SWF sands are amenable toa prediction methology that includes inversion, seismicattributes, and attenuation analysis. Combining these meth-ods with high-resolution multicomponent seismic acquisi-tion and processing should help avoid these costly hazardsand prevent costly well failures in the future. If you are inter-ested in learning more about the PGS/ERCH Shallow WaterFlow Project, contact Gene Sparkman at 1-281-363-7936 orsparkman@erch.harc.edu.

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Figure 12. Multicomponentseismic inversion for a deep-water Gulf of Mexico data setshowing deviation in VP/VSratio from the mud-rock trend.Purple and blue are zoneswith abnormally high VP/VSrelative to expectation, possi-bly indicating sand bodiesclose to failure. Vertical axis isPP time relative to mud line.

Figure 13. AVO analysis showing an abnormally highPoisson’s ratio anomaly at about .9 s in the vicinity ofa well exhibiting shallow-water flow. Red indicatespositive Poisson’s ratio anomalies, and blue indicatesnegative anomalies. The arrow is the well location.

(Continued on p. 1052)

Suggested reading. “Rock physics—the link between rock prop-erties and AVO response” by Castagna et al. (in Offset-DependentReflectivity—Theory and Practice of AVO Analysis, SEG, 1993).“Elasticity of high-porosity sandstones: Theory for two NorthSea data sets” by Dvorkin and Nur (GEOPHYSICS, 1996). “Pressuredifferences between overpressured sands and bounding shalesof the Eugene Island 330 Field (Offshore Louisiana, USA) withimplications for fluid flow induced by sediment loading” byStump et al. (in Overpressures in Petroleum Exploration, Memoire22, Elf EP Editions, 1998). “Percolation of electrical and elasticproperties of granular materials at the transition from a sus-pension to a loose packing” by Marion and Nur (Physica A, 1989).“Compressional velocity and porosity in sand-clay mixtures”by Marion et al. (GEOPHYSICS, 1992). “Critical porosity: A key torelating physical properties to porosity in rocks” by Nur et al.(TLE, 1998). Vibrations of Soils and Foundations by Richart et al.(Prentice Hall, 1970). “Acoustic and mechanical loading ofmarine sediments” by Smith (in Physics of Sound in MarineSediments, Plenum Press, 1974). “Prediction of pore pressuresbefore and after drilling—Taking the risk out of drilling over-pressured prospects” by Traugott and Heppard (in AbnormalPressures in Hydrocarbon Environments, AAPG, 1994). LE

Acknowledgments: Laboratory measurements were made by CarlSondergeld and Bruce Spears at the University of Oklahoma. Seismicmodeling was performed by Surinder Sahai at Conoco. Sahai and SantiRandazzo (PGS) processed the seismic data. Multicomponent seismicinversion was conducted by Carlos Moreno at the University of Oklahoma.Many thanks to Allen Bertagne of PGS Reservoir and Gene Sparkmanand Roger Entralgo of ERCH for coordinating efforts. Thanks to Conocoand PGS Reservoir for permission to publish this paper.

Corresponding author: Alan.R.Huffman@usa.conoco.com

(Huffman, from p. 1035)