50 Oilfield Review

Compaction and Subsidence

Dirk Doornhof Nederlandse Aardolie Maatschappij (NAM) B.V.Assen, The Netherlands

Tron Golder KristiansenBP NorwayStavanger, Norway

Neal B. NagelConocoPhillipsHouston, Texas, USA

Phillip D. PattilloBP AmericaHouston, Texas

Colin SayersHouston, Texas

For help in preparation of this article, thanks to OlavBarkved, BP, Stavanger; Tom Bratton, Denver; Rob Marsden,Gatwick, England; Frank Mitchum, BP, Houston; and MarcThiercelin, Moscow. One author acknowledges permissionto publish this article from ConocoPhillips Norge andcoventurers, including TOTAL E&P Norge AS, Eni Norge AS,Norsk Hydro Produksjon a.s., Statoil ASA and Petoro AS.One author acknowledges permission to publish this articlefrom BP Norge AS and coventurers Hess Norge AS,Enterprise Oil Norge AS and TOTAL E&P Norge AS.ECLIPSE and Sonic Scanner are marks of Schlumberger.CMI Compaction Monitoring Instrument is a mark of Baker Atlas. FCMT Formation Compaction Monitoring Toolis a mark of Halliburton. VISAGE is a mark of V.I.P.S.

Pressure drawdown in a producing field can lead to reservoir compaction, movement

of the overburden and subsidence of the surface above the reservoir. This compaction

and subsidence can prove costly, both for production and surface facilities.

Venice, the Italian city known for the romance ofits canals, is slowly sinking into its surroundinglagoon, mostly due to natural causes. This is animprovement over the recent past: for severaldecades of the 20th century, Venice was rapidlysinking into the lagoon. From the 1940s until the 1970s, extraction of water and natural gas from below the city radically increased thesubsidence rate.1

Subsidence is a sinking of a surface, such asground level, relative to a stable reference point.It occurs naturally as a result of plate-tectonicactivity, above active faults and in places wherefluid is expelled from underlying sediments.Fluid expulsion is common at river deltas, suchas the Po River delta around Venice. This effect,which amounts to a subsidence rate of a fewcentimeters per century in Venice, is distinctfrom eustasy, or a change in sea level, whichaccounts for a rise of about 13 cm [5 in.] percentury in Venice.

After World War II, two practices increasedthe subsidence rate of Venice. First, the amountof water withdrawn from aquifers underlying thecity increased dramatically to accommodate agrowing population. As a result, the water levelsin these aquifers dropped significantly. Secondly,natural gas was extracted from an industrial zoneon the mainland just across the lagoon. Thesubsidence rate measured between 1968 and

1969 had increased from its low historic rate to1.7 cm/yr [0.7 in./yr] in the industrial area and1.4 cm/yr [0.6 in./yr] in the city center.2

This dramatically higher rate of subsidencewas caused by compaction, which is a decrease involume of a reservoir resulting from pressurereduction and production of fluids, in this case,water and gas. The terms compaction and subsi -dence describe two distinct processes.Compaction is a volumetric change in a reservoir,while subsidence is a change of level of a surface.That surface could be a formation top, themudline in a submarine area or a section of theEarth’s surface above the compacting formation,as is the case with Venice.

A record 2-m [6.6-ft] flood submerged Venicein November 1966.3 After the flood, extraction ofboth natural gas and water was essentially haltedaround the city to control subsidence. Aquiferlevels rose again, and the ground rebounded afew centimeters. However, the rebound was only a fraction of the ground-level change that had occurred over the period of water andgas extraction. Today, the slow naturalsubsidence continues.

In the oil and gas industry, some cases ofsubsidence have become well-known. GooseCreek field south of Houston was one of the firstthat received intense study. Subsidence over thatfield was first noticed in 1918, eventuallyreaching more than 3 ft [0.9 m] and submerging

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the Gaillard Peninsula, which lay over the centerof the field.4 The Wilmington field in California,USA, several fields at Lake Maracaibo inVenezuela, and the Groningen field in TheNetherlands all had noticeable subsidence thatrequired remediation because the surface abovethe reservoirs was at or near sea level.5 The chalkfields in the Norwegian North Sea, notablyEkofisk, Eldfisk and Valhall fields, havecompacted, and the resulting subsidence at themudline generated concern for platform safety.Low-strength carbonate reservoirs in NorthwestJava field, Indonesia, and fields offshoreSarawak, Malaysia, have also experiencedsignificant subsidence.6 The Belridge field inCalifornia and neighboring diatomite fieldssubsided and had numerous well failures.7

The economic consequences of compactionand subsidence can be huge, but not all of themare negative. Compaction may be beneficial, as itprovides a potentially strong production-drivemechanism. In this article, we examine theissues relating to compaction and subsidence,illustrated by reservoir-management approachesin the North Sea, The Netherlands and the Gulfof Mexico.

Compaction PhysicsA porous medium, such as a hydrocarbon-producing formation, contains fluid within itssolid structure. This simple observation hasprofound implications when the material isplaced under stress. For example, sedimentdeposited under water may have high porosityimmediately after deposition, and it may behavemore like a liquid with solid material insuspension, rather than a solid material con -taining liquid. As more sediment accumu lates,the original layer must support the weight of thenew material. As long as fluid pathways exist,some of the liquid will be expelled, and porositywill decline.

1. For more on subsidence in Venice: Brighenti G, Borgia GCand Mesini E: “Subsidence Studies in Italy,” inChilingarian GV, Donaldson EC and Yen TF (eds):Subsidence Due to Fluid Withdrawal, Developments inPetroleum Science 41. Amsterdam: Elsevier Science(1995): 248–253.

2. Brighenti et al, reference 1.3. See http://www-geology.ucdavis.edu/~cowen/~GEL115/

115CHXXsubsidence.html (accessed October 17, 2006).4. Pratt WE and Johnson DW: “Local Subsidence of the

Goose Creek Oil Field,” Journal of Geology 34, no. 7–part 1 (October–November 1926): 577–590.

For more on subsidence in fields offshore Sarawak: Mah K-G and Draup A: “Managing Subsidence Risk inGas Carbonate Fields Offshore Sarawak,” paper SPE88573, presented at the SPE Asia Pacific Oil and GasConference, Perth, Australia, October 18–20, 2004.

7. Fredrich JT, Arguello JG, Thorne BJ, Wawersik WR,Deitrick GL, de Rouffignac EP, Myer LR and Bruno MS:“Three-Dimensional Geomechanical Simulation ofReservoir Compaction and Implications for Well Failuresin the Belridge Diatomite,” paper SPE 36698, presentedat the SPE Annual Technical Conference and Exhibition,Denver, October 6–9, 1996.

5. For more on subsidence in Wilmington field and LakeMaracaibo fields: Poland JF and Davis GH: “LandSubsidence Due to Withdrawal of Fluids,” in Varnes DJ:Reviews in Engineering Geology II. Boulder, Colorado,USA: Geological Society of America (1969): 187–268.

6. For more on subsidence in Northwest Java field:Susilo Y, Rahamanda Z, Wibowo W, Tjahyadi R andSilitonga FJ: “Stimulation Efforts in Carbonate GasReservoir Experiencing Subsidence in Offshore NorthWest Java Field—Indonesia,” paper SPE 82264,presented at the SPE European Formation DamageConference, The Hague, May 13–14, 2003.

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As burial depth of a sediment layer increases,the weight of the overlying sediments increases,tending to squeeze fluid out of the layer andreduce its porosity (above). The fluid pressurealso increases with depth. If the overlying stratabecome impermeable to flow and the fluidcannot escape laterally, then as additional burialcompacts the sediment, the fluid pressureincreases beyond hydrostatic.8 This fluid over -pressure can also occur when rapid sedimen -tation rates outpace the expulsion rate of excessfluid from the formation.9

The result of having a pressurized fluid in asolid framework is that both the fluid and thesolid support stresses on the material. This

concept is the effective-stress principle, whichstates that the stress affecting the behavior of asolid material is the applied stress minus thesupport from the pore-fluid pressure.10 Whenfluid is produced from a reservoir, the weight ofthe overburden does not decrease, but the porepressure does, increasing the vertical effectivestress acting on the solid matrix. The degree ofresulting compaction depends on the compres -sibility of the rock and the boundary conditions.

Compressibility relates changes in volume tochanges in applied stress. There are several waysof expressing the compressibility of a porousmedium, but two are commonly used.11 Pore-volume compressibility, Cpv, is a measure of the

change in pore volume caused by a change inapplied stress. Bulk compressibility, Cbv, is ameasure of the change in bulk volume due to achange in applied stress; it is the inverse of thebulk modulus. Under an assumption that thegrains are incompressible, Cbv is the product ofporosity and Cpv. The compressibility valuedepends on the rock composition anddepositional history, and can vary with changingpore-fluid composition.

A competent, granular sandstone typically hasa Cpv value of about 5 x 10-4/MPa [3 x 10-6/psi], butit can exceed 15 x 10-4/MPa [100 x 10-6/psi] forhighly compressible North Sea chalks (below).Grain-bonding cement tends to increase rockstiffness, decreasing its compressibility.

Depositional history is important becausecompaction tends to cause irreversible changesin the rock fabric. Grains shift; clay particlesdeform; cemented bonds break; and even grainscan break under loading. Since these changesare irreversible, the rock displays hysteresis.When stress on the rock decreases, which wouldoccur if some of the overburden weight wereeroded away or if formation pressure increasedwithout additional deposition, the unloadingmaterial is less compressible than when it wasloaded over the same stress interval. Also, theunloaded material is less compressible onreloading until the original stress condition isreached again (next page).12

Several mathematical formulations havebeen developed to model the behavior of rocksunder stress, but to date there is no singleformulation that the industry has accepted abovethe others. The best of these models havemechanisms for elastic and plastic deformations,thermal effects and time-dependent, or creep,effects.13 Some rocks are weaker when at leastpartly saturated with water rather than oil.Although the physical mechanism for that effectis not completely understood, some modelsinclude algorithms to account for the water-weakening effect.

Subsidence PhysicsIt is difficult to observe compaction of ahydrocarbon reservoir, but subsidence at thesurface is often easy to see. Water encroachesupon previously dry land; an offshore platformloses its air gap between high waves and thebottom deck; wellheads and casing may protrudeabove the surface; or surface structures sink.Subsidence has been a primary indicator ofcompaction over oil fields since it was firstnoticed at Goose Creek field in 1918.14

52 Oilfield Review

> Overburden stress and pore pressure. The overburden stress (yellow arrows,right) on a formation increases with depth because of the added weight of over-burden. The overburden stress (yellow line, left) is determined by integrating thedensity of the overburden. The pore pressure (blue) also increases with depth,with a gradient determined by the brine density. Beneath an impermeablestratum (red), the pore fluid becomes overpressured as the formation compactsunder additional weight without being able to release pore fluid.

Pore pressure

Overburden stress

Dept

h

Pressure

> Chalk and sandstone structures. Scanning electron micrographs of outcrop samples show chalkfrom Stevns Klint, Denmark (left) and sandstone from Berea, Ohio, USA (right). The chalk is a weakjumble of uncemented fragments of coccoliths, while the sandstone is a more competent arrange -ment of cemented grains. This structural difference helps explain the extreme difference in compres -sibility between these materials. Note the much higher magnification of the chalk image.

10 µm 50 µmX5,000 X235

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The original engineering report aboutsubsidence at Goose Creek field included adetailed discussion of other suspected causes ofthe local subsidence. However, the report showedthat the effect was not due to the generalsubsidence of the Gulf coast; it was not due to achange in mean sea level; it was not erosion; andit was not a sinkhole caused by dissolution oflimestone, salt or some other soluble formation.Maps of subsidence showed that a depressionfollowed the general outline of the field. By theauthors’ rough calculation, the subsidence bowlaccounted for only 20% of the oil, gas, water andsand that had been removed from the field.However, in the conclusion of the paper, theyimply that the compaction occurred in theoverlying clays, rather than in the producingformation itself.

Over the decades since the Goose Creek study,the understanding of subsidence resulting fromfluid withdrawal has progressed signi f icantly.Subsidence studies today involve detailedreservoir flow and geomechanical analysis, butthe general principles can be explained withoutresorting to a complex model.

The formations involved are divided into fourparts: the compacting volume, the overburden, thesideburden and the underburden. These last twoterms are not generally used except in geo -mechanics, but refer to materials laterallyconnected to the compacting formation and thosebeneath it and the sideburden, respectively.

The compacting volume may include morethan the hydrocarbon-bearing formation. Aquifersbeside or below may also compact as they drain,and should be modeled as part of the compactingformation, albeit with different properties inmany cases.

The decrease in volume caused by com -pacting a buried formation is usually transmittedto the surface. The subsidence bowl is generallywider than the compacted area. The amount thatit spreads depends on the material properties ofthe overburden and the depth of the compactingformation. In addition, if the overburden doesnot expand, the volume of the bowl at surface isequal to the compaction volume at depth.

A subsidence bowl tends to be approximatelysymmetric, even if the compaction in the under -lying volume is not. Because the bowl is asuperposition of subsidence resulting from eachcompacting element, it tends to average out thevariation. Overburden anisotropy from faults ormaterial anisotropy can restrict or change theshape of the bowl; faults can allow slippage,preventing the spread of subsidence.

The overburden can also expand, althoughthis is a minor effect for most overburden rocks.However, this volume change can result in a time-dependent effect as the overlying rockslowly creeps, first in expansion and later in compaction.

When a formation compacts, the sideburdenoften does not, either because it is impermeable,separated from the compacting formation by asealing fault and therefore not experiencing anincrease in effective stress, or simply because itis a stronger material. The overburden weightthat had been supported by the compactingformation can now be supported partially by thesideburden. This creates what is termed a stressarch over the compacting formation. The extentand effectiveness of the stress arch in supportingoverburden are functions of the materialparameters of the over- and sideburden, thelateral extent of the compacting zone and theamount of compaction.

Although the predominant motion in asubsidence bowl is vertical, horizontal move mentsalso occur. The horizontal movement is zero in themiddle and at the outer boundary of the bowl andreaches a maximum, inward displacement inbetween. Large horizontal movements can havedevastating effects on pipelines and otherextensive surface structures unless they aredesigned to accommodate the strain.

Measuring Compaction and SubsidenceSubsidence-monitoring methods differ foronshore and offshore areas. Onshore, bench -marks are common tools of civil engineers. Abenchmark is a survey mark at a known positionand a measured elevation that is used todetermine changes in elevation with respect toother benchmarks. Benchmarks outside of thesubsidence bowl provide fixed reference points.

The most accurate way to determine anelevation difference between benchmarks is toconnect two locations with a liquid-filled tube.The hydrostatic level will be the same at bothends of the tube, so changes in relative elevationcan be determined with great accuracy. However,performing this type of survey over large areascan be prohibitively expensive. Most benchmarksurveys compare elevation by sighting though atransit or using a laser, after careful leveling ofthe instrument. This method can also be used toobtain relative elevation changes betweenplatforms within a complex.

Tiltmeters—devices that are sensitive to thechange of angle on the surface or in wells—canprovide subsidence data for onshore locations.These devices are also used to monitor theadvance of an induced fracture.15

8. Hydrostatic pressure is the magnitude of pressurecaused by the weight of the overlying column of brine,often obtained by integrating the brine density fromsurface to the depth datum.

9. Other geologic processes can also generate over -pressure or underpressure situations; examples includechemical diagenesis, regional uplift or downthrust, andhydrocarbon migration.

10. The relationship is also called the net-stress principle: σ = S – αP, where σ is the net or effective stress on the solid material, S is the stress applied to the body, P is the pore pressure and, in isotropic elastic solids, α = 1 – Kb/Ks. Here, K is the bulk modulus, and this lastterm is the ratio of the bulk moduli of the rock (b) and themineral grains in the rock (s). In highly porous and weakmaterials, the grain modulus is much greater than therock modulus, so α is approximately 1, and σ ≈ S – P.Both σ and S are tensors, so this equation applies in allthree principal directions.

11. For a complete definition of the types of compres -sibilities: Zimmerman R: Compressibility of Sandstones,Developments in Petroleum Science 29. Amsterdam:Elsevier Scientific Publishing Company, 1991.

12. For a study of field stresses with pressure cycling:Santarelli FJ, Tronvoll JT, Svennekjaer M, Skeie H,Henriksen R and Bratli RK: “Reservoir Stress Path: TheDepletion and the Rebound,” paper SPE/ISRM 47350,presented at the SPE/ISRM Eurock ’98 Symposium,Trondheim, Norway, July 8–10, 1998.

13. A deformation is elastic if, after a stress change, amaterial returns to its initial shape when the stressesreturn to the initial condition. Deformations that result in a permanent change in shape after such a stresscycle are termed plastic, or inelastic. Creep describes a deformation that continues after the stress change stops.

14. Pratt and Johnson, reference 4.15. Bennett L, Le Calvez J, Sarver DR, Tanner K, Birk W,

Waters G, Drew J, Michaud G, Primiero P, Eisner L,Jones R, Leslie D, Williams MJ, Govenlock J, Klem RC and Tezuka K: “The Source for HydraulicFracture Characterization,” Oilfield Review 17, no. 4(Winter 2005/2006): 42–57.

> Compaction hysteresis. Increasing the netstress on a material that is in a plastic statecauses a rapid decline in volume (1). If thematerial is unloaded, the volume rebound is notas large as the collapse was, and it is often closeto the elastic response (2). Reloading the materialinitially causes a quasi-elastic response, until theprevious high net-stress state is reached (3). Atthat point, the material again follows the plastic-failure line.

Net stress

Pore

volu

me

1

3

2

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Global positioning system (GPS) stations canbe used for fixed positions either onshore oroffshore. Under ideal conditions, GPS techniquescan detect elevation changes of about 2 mm.

Another method that is under evaluation byseveral companies uses satellites for subsidencemonitoring. Interferometric synthetic apertureradar (InSAR) relies on repeated imaging of agiven geographic location by air- or space-borneradar platforms. With complex measurements—including magnitude and phase—of radarimages of the same area, one can construct aninterferogram from the difference in phase of thereturn from each point. The phase differencesare sensitive to topography and any intrinsicchange in position of a given ground reflector.

The change in distance is along the line ofsight to the satellite, preventing it from directlydistinguishing vertical and horizontal movement.However, over a compacting reservoir in alocation without other tectonic movement, thechange is assumed to be due to subsidence, andprimarily vertical.

Benchmark reflectors can be established forInSAR, but a more widespread set of measure -ments can be obtained by using existing objectsthat scatter the radiation, such as roadintersections or rooftops pointing in theappropriate direction. Any movement of thesepermanent or persistent scatterers that isunrelated to subsidence is generally not known,but the sheer quantity of reflectors compensatesfor that deficiency.

The InSAR method has limitations. Growth ofvegetation between satellite passes can causeinterpretation problems over open fields. Rapidchanges in elevation, such as occur near activefaults, are easier to measure than slowsubsidence. Distance measurements can bemade when the satellite is ascending or when itis descending. Since the angle of reflection isdifferent, the two measures generally involvedifferent sets of scatterers. The ascending anddescending measurements of subsidence maynot agree completely.16

Offshore, the subsidence bowl is not so easilyaccessed. Most commonly, subsidence is moni -tored at platforms. This is not merely aconvenience, but a necessity. The air gap, ordistance between mean sea level and the loweststructure of the platform, has to remain greaterthan the wave height. Companies use astatistically derived wave height, often themaximum wave height expected over a 100-year period.

The air gap can be measured by severalmethods, all of which rely on a known benchmarkon the platform. Continuous measurement ofdistance to the water can be obtained acous -tically; alternatively, an underwater pressuretransducer mounted on the leg of the platformcan indicate the height of the water columnabove it. Interpretation of these two methodsrequires knowledge of sea level at the time of themeasurement, which means tides and wind-driven waves have to be considered.

Today, the most common method fordetermining platform subsidence is by usingGPS, as is done onshore. Some interpretationmethods require a nearby platform that is notsubsiding, but the methodology is improving, andsome companies that provide this service to theindustry now claim their interpretation does notrequire a near, fixed benchmark.

Subsidence affects pipelines and otherstructures on the seabed. Bathymetry surveys arethe most direct way to map the extent of anundersea subsidence bowl. The survey indicateswater depth with respect to sea level. This isgenerally obtained by bouncing an acousticsignal off the mudline and back to a receiver. The traveltime measurement must be correctedfor the effects of water salinity and temperature.Repeat surveys can monitor the development of asubsidence bowl.

Formation compaction is usually moredifficult to measure than subsidence. Shallowcompaction that results in subsidence on landcan sometimes be seen directly, when wellheadsof shallow wells protrude farther and fartherfrom the surface. This is the case in Mexico City,where the shallow aquifers have compacted andsome well casings are around 5 m [16 ft] higherthan when installed.17

The most common method for measuringcompaction in deep formations is through use ofradioactive bullets, or markers (left). With aspecial perforating gun, the bullets are fired intoa formation at known intervals, such as 10 m[32.8 ft]. Each marker contains a low-strength,long-lived radioactive source, generally cesium.Specialized wireline logging tools, such as theSchlumberger Formation Subsidence MonitoringTool (FSMT), Baker Atlas CMI CompactionMonitoring Instrument or Halliburton FCMTFormation Compaction Monitoring Tool, measurethe relative positions of the radioactive markeraccurately. Compaction-monitoring tools containthree or four detectors: two at the top of thesonde and one or two at the bottom. The meanspacing between the top and bottom detectors is

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>Monitoring radioactive bullets. A sonde withfour gamma ray detectors minimizes the effect ofunintentional tool movement by detecting tworadioactive markers (RM) almost simultaneously.The bullet separation, S1, S2 and S3, should beapproximately equal to the mean separationbetween the top and bottom pairs of detectors.

Detector 1

Detector 2

Detector 3

Detector 4

RM

RM

RM

RM

S1

S2

S3

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roughly the same as the spacing between themarkers. This minimizes distance errors due toany tool movement from the wireline cablestretching and contracting. Repeat surveysindicate the change in separation of the markers.

The best place to put markers is in a verticalmonitor well. Deviated wells introduce an errorin the position of the marker, depending on theorientation of the gun when the bullets are fired. Producing wells may also flow formationsolids, introducing uncertainty about the causeof the marker movement—either compaction or solids production.

In the past, other methods were used forcompaction monitoring, but most of them havebeen discontinued as insufficiently accurate.These include time-lapse logging for casing collarlocation and for petrophysical markers. Time-lapse seismic studies can also be used as tools formonitoring subsidence of subsurface formationtops. Although the method is generally tooimprecise for accurate compaction monitoring,the extensive coverage of reservoirs provided byseismic surveys makes them useful for reservoirmanagement. Subsurface movement can also beindicated by using microseismic arrays thatdetect and locate noise generated by compactingand yielding rock.

Vital input for compaction studies also comesfrom core measurements. A load frame stresses orstrains a core sample and measures its response,including pore-volume changes, pore-pressurechanges, length and diameter. These tests canalso examine the effect of changing fluids ortemperature on rock deformation and strength.Stress or strain boundary conditions similar tothose expected in the field can be applied.

Two common laboratory conditions arehydrostatic-stress and uniaxial-strain boundaryconditions. In the hydrostatic-stress condition,all three principal stresses are equal. This is thesimplest of the compressibility conditions to

apply, but is not representative of actual fieldconditions. The uniaxial-strain condition main -tains a constant sample cross-sectional area,while the axial stress changes either throughaxial loading or reduction of pore pressure in thesample. Although this condition is felt to becloser to the boundary conditions in some fields,studies of changes in horizontal stresses causedby depletion in both the Ekofisk and Valhallchalk fields indicate some other boundarycondition applies.18

The Impact of Compacting FormationsDespite a necessary focus on damage to wells and facilities caused by compaction and subsi -dence, the positive effect on production cannotbe ignored. In the weak chalks of the North Seaand the diatomites of California, the so-calledrock drive can be many times greater than fluid-expansion drive. Formation permeabilitycan either increase or decrease, because open fractures can close or new fractures can be generated. Matrix permeability generallydecreases as the pore spaces collapse or grains break.

The weakened material can flow into awellbore. This happened most notably early inthe history of the Norwegian chalk fields, wherethe chalk flowed like toothpaste.19 A betterunderstanding of chalk failure led to improvedproduction methods that mitigated this behavior.In sandstone formations, sanding can be acommon response of a mechanically weakmaterial during production. Fracturing andborehole breakouts can also occur.

Casing collapse has been an ongoing problemin fields with large amounts of compaction. Acompacting formation pulls the cemented casingalong with it, compressing the axial dimension ofthe casing. However, above the formation, theoverlying material typically elongates, and thecasing there stretches. In either situation, thestress on the casing can exceed its mechanicalstrength and cause collapse within thecompacting zone or fail in tension in theoverburden. Shear failure and casing crushingcan occur. Faults in the overburden also canreactivate because of differential movement, andbedding planes may have differential slippage.Both types of events may shear a wellbore thatlies within an area of differential movement.

On the surface, remediation can also becostly. Since 1987, about US$ 3 billion has beenspent to counter the effects of subsidence overthe Ekofisk field, first raising the platforms 6 m[19.7 ft] and later replacing the platform complex.

The bowl formed by subsidence affectspipelines, roads and other structures. Lateralmovement within the bowl can generate damage.Some of this damage can be mitigated byconstruction design, such as strain-relief loops inpipelines. However, a fault extending to thesurface can generate step-offsets resulting indamage to structures crossing the fault.

Surface effects of subsidence can beextensive, particularly in low-lying areas nearlarge bodies of water. For example, dike systemswere constructed and repeatedly extended as thedepression over the fields at Lake Maracaibogrew.20 The Netherlands has an extensive dikeand canal system; over the subsiding Groningenfield, the ground level is monitored and the dikesystem enhanced as needed. Wilmington,California, took a different approach, mandatinga waterflood in the field underlying the city,which successfully stopped the subsidence.

In the subsurface, drilling and completionpractices must account for the effects ofcompaction. Field experience can indicate areasthat should be avoided in well paths, such asfaults. This may be as simple as changing thewellbore trajectory somewhat or as complex andexpensive as adding platforms to reach remoteparts of a field. Heavy-walled tubulars cansustain additional strain, but often require acost-benefit analysis to compare their useagainst accepting a shorter well life.

In new developments, many of thesedecisions must be made in advance of designingfacilities. Information from exploratory drillingand offset wells are used to develop models tohelp in these decisions.

Simulating a Compacting ReservoirThe behavior of a mechanically dynamic reservoirrequires more sophisticated modeling than thepressure-dependent pore volume that is includedin most flow simulators. Volume units cancompact or stretch and can also change shape.

Historically, reservoir flow simulation and geomechanical simulation were doneseparately.21 However, the physical parameters,particularly pore pressures, are affected by bothflow dynamics and mechanical deformation. As afirst approximation, one model is run first and itsresults are used as input for the other model. Thefirst model typically is a flow simulation, becauseit runs more quickly. With no feedback to the firstmodel, this approach is considered to beuncoupled, and the resulting output of the samevalue—such as pore pressure—of the twomodels can be divergent.

16. InSAR has also been used to measure uplift. Forinformation on satellite measurements of grounddeformation around the volcanic caldera of YellowstoneNational Park, Wyoming, USA: http://volcanoes.usgs.gov/yvo/2006/uplift.html (accessed September 29, 2006).

17. Poland and Davis, reference 5.18. Goulty NR: “Reservoir Stress Path During Depletion of

Norwegian Chalk Oilfields,” Petroleum Geoscience 9, no. 3 (2003): 233–241.

19. Simon DE, Coulter GR, King G and Holman G: “North SeaChalk Completions—A Laboratory Study,” Journal ofPetroleum Technology 34, no. 11 (November 1982):2531–2536.

20. Poland and Davis, reference 5: 214–216.21. Here, to distinguish between conventional reservoir

simulation, which includes complex flow dynamics andsimple geomechanics, and geomechanical simulation,which has an opposite emphasis, the conventionalsimulation is referred to as a flow simulation.

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The next level of modeling typically uses aflow simulator to solve a time-step first—again,because it runs faster—and feeds those resultsinto a geomechanical simulator. If the compa -rable values from the two models do not agreewithin a given tolerance at the end of the time-step, parameters are adjusted and the time-stepis rerun until they do agree. These iterationscontinue through subsequent time-steps of thesimulation run. This method is termed looselycoupled. It requires more computer time but alsoproduces results that are in closer agreementbetween the two simulators.

Both flow and mechanical modeling aremathematically complex, and combining the twointo one simulator was difficult to achieve. Today, some simulators can carry out simul -taneous flow and geomechanics solutions,including Schlumberger ECLIPSE Geomechanicsreservoir simulation software, V.I.P.S. VISAGEmultiphase stress dependent reservoir simu -lator and a few that oil companies, such asConocoPhillips, or universities have developedin-house. This type of simulation is often referredto as fully coupled. These models are still not run as a standard, because they are consider -ably slower than uncoupled and loosely coupled models.

Waterflooding to Repressurize a Chalk FieldWaterflooding has been a recovery method in theE&P business for many years, either to displacehydrocarbons or to maintain the pressure neededto keep oil or gas in single phase. It has also beenused to mitigate subsidence, such as in theWilmington field, which sits under the harborarea of Long Beach, California. Severe subsi -dence at this economically important locationled to a massive waterflooding program in thefield that resulted in about a foot of rebound.22

Waterflooding has also been successful in theEkofisk field, a huge chalk structure draped overa salt dome, with approximately 6.7 billion bbl[1 billion m3] of original oil in place. In 1969,Phillips Petroleum, now ConocoPhillips, madethe first discovery in the Norwegian sector of the North Sea for the Ekofisk partnership. Thefield still produces more than 300,000 bbl/d[47,700 m3/d] of oil and more than 250 MMcf/d[7 million m3/d] of gas.

The crest is approximately 2,900 m [9,500 ft]below sea level, in 78-m [256-ft] deep water.Field production comes from both the Ekofiskformation, which contains two-thirds of thereserves, and the underlying Tor formation. Athin, impermeable chalk, called the Tight Zone,separates the two formations.

Porosity in both formations ranges from 25%to greater than 40% in producing areas of thefield, and the productive zone can be as thick as150 m [490 ft] within the crest of the field. Chalkup to about 50% porosity has been encounteredin the field. Preservation of such high porosity atthe depth of the reservoir is attributed tosignificant overpressuring and the earlyemplace ment of hydrocarbons.

By 1984, platforms in Ekofisk field hadsubsided several meters, and many wells hadfailed. The operator began monitoring platformsubsidence and obtained new bathymetry surveys

of the mudline. Company scientists performeddetailed geomechanical studies of core samplesand created field models. They discovered thatchalk compaction is extreme in this field: adecrease in formation pressure from thediscovery value of 7,200 psi [49.6 MPa] to apotential abandonment condition at 3,200 psi[22 MPa] would result, for example, in a decreasein porosity from 38% to about 33% (above).

Chalk behavior depends on its stress state. Atlow confining and shear stresses, chalk is elastic,and a small decrease in formation pressureinduces only a small elastic strain. However, alarge decrease in formation pressure causes

56 Oilfield Review

> Ekofisk chalk model. The chalk model is depicted on a plot of generalizedshear stress against average effective stress (top). The material cannot goabove the shear-failure line because it will fail in shear. The endcaprepresents the boundary between elastic (inside) and plastic (outside)behavior. If the stress condition is on the endcap (at Start), increasing itmoves the endcap outward. Decreasing the stress (to End) moves thecondition back into the expanded elastic zone. The behavior at the endcapcan be seen in the chalk type curves for the field, showing the decrease inporosity with increasing effective overburden stress (bottom). The chalkinitially behaves quasi-elastically, with a small porosity decrease. When thematerial crosses the endcap, the porosity declines more rapidly. The initialendcap location is porosity-dependent (dashed line), with lower-porositychalks having a larger initial elastic region.

Average effective stress, psi

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inelastic deformation and substantial strain. The onset of inelastic behavior occurs at theendcap, a surface in stress space that connects tothe shear-failure line at high shear stresses.However, inelastic compaction alters the chalk,moving the endcap location to the highereffective-stress condition.

As a result of compaction, the subsidencerate in the mid- and late-1980s was about30 cm/yr [1 ft/yr]. The resulting loss of air gapand potential impacts on platform safety becamea major concern. The 6-m increase in platformheight in 1987 was performed to increase the airgap between the lower decks and the expectedmaximum wave height.

In 1980, waterflooding was not initiallyconsidered a viable option in the Ekofisk fieldbecause tests indicated that the chalk was atbest intermediate-wet and at worst oil-wet,reducing the water imbibition that aids water -flood efficiency. Nonetheless, the Ekofiskpartnership felt the potential production gainswarranted a small waterflood pilot, which wasinitiated in 1981.23 The results from the pilotwaterflood suggested good oil displacement andlimited early water breakthrough.

Operator Phillips, now ConocoPhillips, beganstaging a full-field waterflood in 1987. It wasdesigned as a production enhancement mech -anism, with voidage balance achieved in 1994.Despite this, the subsidence rate remainednearly constant as waterflooding continuedunder voidage balancing, reaching a maximumrate of 42 cm/yr [16.5 in./yr] in 1998 (above right).

A new complex of platforms was installed,both to withstand the continuing subsidence andto provide more facilities for an expansion offield activities.24 During the changeover from theold platform complex to the new Ekofisk IIcomplex in late 1998, water injection continuedwhile production was halted for several weeks.During this period, and continuing since then,the subsidence rate decreased dramatically to acurrent rate of 15 cm/yr [5.9 in./yr] (right). Whilea reduction in subsidence rate such as this hadbeen considered by the operator as a possibility,

its magnitude was unexpected, based on the fieldsubsidence history.

The voidage balancing condition achievedduring the mid-1990s should have slowed themechanical compaction, because the effectivestress was no longer increasing. With voidagebalancing, and later repressurization, companyscientists expected the formations to stop

compacting in that time period, and perhapsrebound slightly, but this did not happen.Although creep in the overburden can cause adelayed reaction between compaction andsubsidence, the time delay would not be years, asseen with the subsidence-rate decrease thatfinally began in 1998.

22. Colazas XC and Strehle RW: “Subsidence in theWilmington Oil Field, Long Beach, California, USA,” in Chilingarian GV, Donaldson EC and Yen TF (eds):Subsidence Due to Fluid Withdrawal, Developments inPetroleum Science 41. Amsterdam: Elsevier Science(1995): 285–335.

23. Thomas LK, Dixon TN, Evans CE and Vienot ME: “Ekofisk Waterflood Pilot,” Journal of PetroleumTechnology 39, no. 2 (February 1987): 221–232. Originallypaper SPE 13120, presented at the SPE Annual Technical Conference and Exhibition, Houston,September 16–19, 1984.

24. For more on the Ekofisk platform complex upgrade:“Ekofisk Phase II Looks to the Future,” Journal ofOffshore Technology 5, no. 4 (November 1997): 27–29.

> Ekofisk field production history. The oil rate (green) declined until large-scale water injection (blue)began in the late 1980s. The average reservoir pressure (dashed curve) also decreased until thewater-injection rate increased in 1995. However, the subsidence rate (red) at the hotel, or quarters,platform did not decrease until production was shut in during the transition to the Ekofisk II complexin 1998.

Prod

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01971 1975 1979 1983 1987 1991 1995 1999 2003 2007

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> Subsidence and pressures in the Ekofisk field crestal area. Pressure measurements in wells in thecrestal area follow a trend (blue) with a rapid increase in mid-1998 that corresponds closely to theslowing of the subsidence rate (red).

Pres

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The answer to the timing of the subsidence-rate decrease lay in a chalk-water interaction.Rapid compaction was seen in a dedicatedEkofisk compaction-monitoring well when thewater front moved through the area (left). Inlaboratory tests, chalk compacts more whensaturated with water than when saturated withoil.25 An even more dramatic effect occurs when astressed chalk sample with virtually no initialwater saturation is flushed with seawater. Thesample compacts immediately upon contact withthe flood front, and a compaction front followsthe flood front through the core.26

Water changes the constitutive properties ofthe chalk and mechanically weakens it. Thechalk-water effect is modeled as a movement ofthe endcap that divides noncompacting, elasticbehavior from compacting, plastic behavior. Theeffect of increasing water saturation is to movethe endcap toward a lower stress state,decreasing the size of the elastic region with aminimal change in the stress condition. This isan unstable condition, so the chalk compacts asthe endcap moves to accommodate the currentstress condition. An equilibrium condition isachieved when the stress condition lies along theendcap (next page, top). Although the physicalmechanism for this behavior is not completelyunderstood, it appears to be related to ionexchange at intergranular contacts, leading todecreased cohesion of the chalk.27

This explanation applies to the Ekofisk fieldduring the waterflood voidage-balancing period.The balance between water-induced compactionand a slow increase in support from pressurefavored compaction, so the subsidence rateremained high. The period of injection withoutfluid withdrawal during the Ekofisk IIinstallation in 1998 allowed sufficient pressurebuildup—and effective stress decrease—tomove the formation condition far enough insidethe endcap that the balance shifted, and thesubsidence rate declined. The continuingreservoir compaction after a several thousand-psi pressure increase is attributed to the ongoingbalance between chalk weakening due to contactwith seawater and the decreasing effective stressassociated with reservoir repressurization (left).

ConocoPhillips compares field measurementsof compaction and subsidence to results fromloosely coupled geomechanical and flow modelsdeveloped in-house. The current lower subsi -dence rate means concern for the loss of air gapand its impact on platform safety has beenrelieved somewhat. In addition, the emphasis inmodeling has turned to optimizing field

58 Oilfield Review

0 10 20 30 40

9,600

9,7009,800

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Torformation

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Well 2/4C11A

0 10 20 30 40Compaction rate, cm/yrCompaction rate, cm/yr

October 1986 toSeptember 1992

June 1994 toJune 1996

> Subsidence from depletion and from water effect. Until 1989, allsubsidence at the hotel complex was due to pressure depletion. After theinjection rate balanced the voidage rate in 1994, the subsidence was all dueto water-induced compaction. Both effects were in play in the periodbetween these events.

1

2

3

4

5

6

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8

9

Year

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Depletion only

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1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007

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begins

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begins

< Dedicated compaction monitoring inWell 2/4C11A. This crestal well (field map)was designed as a monitor well equippedwith radioactive markers and had noproduction. Compaction is measuredfrom the top of the markers and convertedto an annual rate (bottom left and right).Since these numbers are cumulative, avertical slope—such as in the Tight Zonenear 10,100 ft—indicates no compaction.Between 1986 and 1992, both the Ekofiskand the Tor formations compacted signif-icantly (left). When the waterflood frontpassed the well, in the period from 1994to 1996 (right), most of compactionoccurred within about 100 ft [30 m] of the Tight Zone, while the Ekofisk and Torformations compacted slowly, or evenstretched slightly as indicated by theleftward slope with depth below 10,500 ft.

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management, for example, using the models tohelp place new wells. Some of these new welllocations are determined through time-lapseseismic studies that track the waterflood front.

The dynamic nature of field managementmeans that a deterministic subsidence modelshould be used with care. For example, theaddition of new well slots in the Ekofisk IIcomplex allows additional drainage of the field,invalidating older subsidence models thatassumed fewer wells. On a smaller scale, wellfailures lead to lost production, and a replace -ment well may be relocated to another part of thefield, both of which affect subsidence predictions.

ConocoPhillips runs a number of modelsbased on different scenarios to obtain aprobabilistic view of reservoir performance,highlighting the 10%, 50% and 90% likelihoodscenarios, termed P10, P50 and P90, respectively(below right). One of the main variables in thesimulations is reservoir-management scenarios,such as the timing of secondary depletion, orblowdown—when waterflooding stops andpressure is allowed to decline again. In additionto the influence of well failures and changes inthe number of producing wells alreadymentioned, the potential uses of CO2 or airinjection also potentially affect subsidencepredictions. With this in mind, the subsidencemodel has to be updated regularly to reflectongoing changes in reservoir management.

Time-Lapse Monitoring of CompactionThe Valhall field is a large chalk field about21 km [13 mi] south of Ekofisk field in theNorwegian sector of the North Sea. It also hasexperienced significant reservoir compactionand seabed subsidence. The upper producingformation, the Tor formation, has originalporosity exceeding 50% in places, and the morecompetent Hod formation has porosity as high as 40%. Production by operator Amoco, now BP,began in 1982, and seafloor subsidence at theplatform complex in the center of the field nowexceeds 5.6 m [18.4 ft]. The current subsidencerate is about 20 cm/yr [7.8 in./yr]. Production todate has been in excess of 550 million bbl[87 million m3], with almost an equal amount ofproducible reserves remaining in place.28

25. Sylte JE, Thomas LK, Rhett DW, Bruning DD andNagel NB: “Water Induced Compaction in the EkofiskField,” paper SPE 56426, presented at the SPE AnnualTechnical Conference and Exhibition, Houston, October 3–6, 1999.For a detailed discussion of early work on water-inducedcompaction: Andersen MA: Petroleum Research inNorth Sea Chalk, Joint Chalk Research Monograph, RF-Rogaland Research, Stavanger, 1995.

26. Andersen MA: “Enhanced Compaction of Stressed North Sea Chalk During Waterflooding,” presented atthe Third European Core Analysts Symposium, Paris,September 14–16, 1992.

27. Korsnes RI, Strand S, Hoff Ø, Pedersen T, Madland MVand Austad T: “Does the Chemical Interaction BetweenSeawater and Chalk Affect the Mechanical Properties of Chalk?,” presented at Eurock 2006, Liège, Belgium,May 9–12, 2006.

28. Barkved OI and Kristiansen T: “Seismic Time-LapseEffects and Stress Changes: Examples from aCompacting Reservoir,” The Leading Edge 24, no. 12(December 2005): 1244–1248.For an overview of Valhall field: Barkved O, Heavey P,Kjelstadli R, Kleppan T and Kristiansen TG: “ValhallField—Still on Plateau After 20 Years of Production,”paper SPE 83957, presented at the SPE OffshoreEurope 2003, Aberdeen, September 2–5, 2003.

>Water-induced chalk compaction. Producing from the chalk increases the average effective stress(from red circle at Start) and moves the elastic envelope outward. Waterflooding alters the materialstate; if the stress condition were allowed to change, the endcap would shrink (gray shading).However, the imposed stress condition (blue circle) has not changed, so the material deforms bycompacting rapidly, essentially keeping the endcap in its original position. In a porosity-stress typecurve (inset), this waterflood-induced behavior appears as a volume loss at constant stress, which isa departure from the behavior without waterflood (dashed curve). The volume change might occurover an extended time period, particularly in low-permeability chalk.

Gene

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> Probability models for Ekofisk field. Subsidence results depend on the field-management plan for the field, so multiple subsidence models have been run.Results of the 10%, 50% and 90% likelihood models (P10, P50 and P90,respectively) are shown, with other results represented by the shaded area.The primary parameter causing difference in these models is the date tobegin secondary depletion, or blowdown (diamonds).

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Well failures were a serious problem,particularly in the 1980s. They were linked toformation compaction and subsidence in theoverburden. The operator has used severalmethods of time-lapse evaluations to understandfield behavior.

In 1982, the first development well, 2/8-A1,was drilled directly beneath the platformcomplex. In 1993, the well failed and wasreplaced by another vertical well, the 2/8-A1A,approximately 60 m [200 ft] away. The operatorobtained a vertical seismic profile (VSP) when

drilling each of the wells. The 60-m separation isclose enough that the results can be compared(above).29 The difference in the traveltimebetween the 1982 and 1993 surveys indicates adecrease in velocity that increases with depth,down to the middle Eocene. This change intraveltime is consistent with stretching of theshale formations.

Both the A1 and A1A wells were equippedwith radioactive markers to monitor formationstrain; the A1A well has markers in severalintervals in the overburden shale. Results in the

overburden from CMI Compaction MonitoringInstrument measurements are consistent withextensional strain that is greater just above theproducing chalk and declines upward.

The crestal area of the field is highlyproductive. Both the geomechanical model andthe VSP results indicate the same anomaly in thisarea. Just above the reservoir around Well A1Athere is some overburden compaction andtraveltime speedup where one would expectextension and traveltime slowdown. This couldbe the result of drainage from the overburden or

60 Oilfield Review

29. Kristiansen TG, Barkved OI, Buer K and Bakke R:“Production Induced Deformations Outside the Reservoirand Their Impact on 4D Seismic,” paper IPTC 10818,presented at the International Petroleum TechnologyConference, Doha, Qatar, November 21–23, 2005.

30. Graben are fault blocks that are downthrown relative totheir surroundings, and horsts are the adjacent upthrownblocks. A horst and graben structure is typically formedby normal faulting in areas of rifting or extension.

31. Kristiansen TG, Barkved O and Pattillo PD: “Use ofPassive Seismic Monitoring in Well and Casing Design inthe Compacting and Subsiding Valhall Field, North Sea,”paper SPE 65134, presented at the 2000 SPE EuropeanPetroleum Conference, Paris, October 24–25, 2000.

32. Kristiansen TG: “Drilling Wellbore Stability in theCompacting and Subsiding Valhall Field,” paperIADC/SPE 87221, presented at the 2004 IADC/SPE DrillingConference, Dallas, March 2–4, 2004.

33. Sayers CM: “Sensitivity of Time-Lapse Seismic toReservoir Stress Path,” Geophysical Prospecting 56,no. 3 (May 2006): 369–380.Sayers CM: “Stress-Dependent Seismic Anisotropy ofShales,” Geophysics 64, no. 1 (January–February 1999):93–98.Holt RM, Bakk A, Fjær E and Stenebråten JF: “StressSensitivity of Wave Velocities in Shale,” ExpandedAbstracts, Society of Exploration GeophysicistsInternational Exposition and 75th Annual Meeting,Houston, November 6–11, 2005: 1593–1596.

> Overburden stretch in the Valhall field. One-way traveltimes from a vertical seismic profile (VSP) in Well 2/8-A1 obtained in 1982 weresubtracted from similar measurements in 2/8-A1A, obtained 60 m away in 1993 (right). The increasing traveltime is thought to becaused by a stretching in the overburden. Radioactive markers in the 2/8-A1A well show that stretching continues from 1993 throughthe most recent CMI survey in 2002 (inset, right). A loosely coupled geomechanical model over the period from 1992 through 2002confirms this behavior (left). In this model, shades of red represent compression, and shades of blue are extension. The sectionbetween the middle Eocene and the top of the reservoir may be showing a local stress arch, with the traveltime change stopping andthen reversing, and the geomechanical model result showing compaction.

2/8–A1

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0 0.500.25

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a stiffer lithology that does not stretch as easily, but most likely results from a local stress-arch effect.

The Valhall field is a patchwork of horsts andgraben, with chalk thin above the horsts andthick over the graben.30 The amount ofcompaction in any area is related to the chalkthickness, among other factors, so the degree ofcompaction across the field is also a patchwork.There is a similarly complex response in theoverburden model results, including local stressarches (right).

Differential movement in the overburden canreactivate existing faults, potentially causingwell failure. Measured microseismic eventscorrelate with locations of these faults.31 Anextensive study of overburden well failures ledoperator BP to abandon an extended-reachdrilling program based at platforms in the centerof the field in favor of unmanned satelliteplatforms in the north and south flanks of thefield.32 Wells from these platforms could avoidmajor faults in the highly compacting centralportion of the field.

BP developed complex rock physics modelsfor Valhall in the chalk and in the overburden.The overburden geomechanical model includesfailure criteria specific to the shales andparameter values that depend on distance fromthe compacting formation. Anisotropy param -eters, which vary as a function of stress path,change because of localized unloading in theshale when a stress arch forms.33

The dynamic response of the Valhall field toproduction and the large volume of remaining oilin place led BP to install a permanent array ofseismic receivers in the seabed over the field in2003. This life of field seismic (LoFS) projectallows BP to repeat seismic surveys several timesa year. The company can follow compactionchanges in and around the reservoir every few months.

The LoFS response can also be used tomonitor production around specific horizontalwells. For example, a horizontal well was addedin an area that had several existing andabandoned producers. After a period of12 months, the time-lapse seismic results showedan expanded compaction zone around the well.The production estimated from producing zonesin that well compared reasonably well with aproduction-logging tool response (right).

These time-lapse seismic studies also showedpossible stress arching near a horizontal well. Thecompression and extension seen in these crosssections echoed similar results BP obtained from

> Horsts and graben. The Valhall field contains horst and graben structuresthat affect the geomechanical model results. This composite image has avertical section above the red line and a near-horizontal view following thetop chalk below the red line. The model output is shown as velocity changes;increase is shown in red and yellow, and decrease is shown in blue. Thesecolors also correspond to compaction (yellow and red) and extension (blue).The horst and graben structure of the field results in alternating areas ofcompaction and extension in the vertical section due to differential formationcompaction and formation of arches in the overburden.

2/8–A–8_A_T2

2/8–A–30_B

> Comparing time-lapse seismicsurveys and production logging.The 18-month time-lapse seismicsurvey (bottom) locates severalhorizontal wells in this part ofthe field with depletion indicatedby acoustic impedance differ-ence, which relates to compaction(increasing from orange to yel-low to green). The horizontalwell near the top of this imagehad several perforated zones(filled circles). The majority ofthe production comes from thetoe of the well, as determinedby a production logging tool(PLT) at low (blue) and high (red)flow rates (bar chart). An esti-mate based on the change inacoustic impedance also yieldsa reasonable prediction of flowrate (green).

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a fully coupled flow and geomechanical model ofValhall field (above).34

Models of Valhall field have predicted aquicker pressure decline than that typically seenin the field. However, the formation pressure ofthe fully coupled model was closer to the slowfalloff seen in the field. BP saw more localarching in the fully coupled model, which helpsto explain the difference between coupled anduncoupled models.

The slower pressure decline results from theslow drainage in this chalk formation with lowmatrix permeability. Above compacting chalk, as

that near a producing well, the overburdenstretches and a stress arch forms, redistributingstresses laterally to chalk at a distance from thewell. This added load deforms that distant chalkand increases its pore pressure, but the tightchalk acts as a choke that is only partially open,preventing rapid drainage to the wellbore. Thissimultaneous determination of pressure, volumechange and permeability requires full coupling tooccur in the simulation. BP engineers found thatthis mechanism occurs at smaller scales—downto sets of pores—and at larger scales betweenhorst and graben structures. The company isseeking ways to incorporate this behavior in thesimpler models.

These examples show the importance that BPplaces on the LoFS results. The operator believesthat multidisciplinary integration of seismicresults with other subsurface data is needed tocapture the value of these frequent time-lapseseismic results.35

62 Oilfield Review

> Stress arching and pressure effects in the Valhall field. Reservoir engineers have had difficulty matching the pressure decline using conventionalmodeling. An uncoupled model using an ECLIPSE flow model with a VISAGE mechanical model had a pressure decline that was more rapid than thatexperienced in the field (top left). Loosely coupling these models resulted in a slower pressure decline. Two versions were run, using either 5 or 25 flow-model iterations between each geomechanical-model step. With the VISAGE VIRAGE fully coupled model, the pressure decline was even slower and morein line with field experience, using both an elastic (E) and a plastic (P) geomechanical formulation. This fully coupled model allowed BP to understand theprocess (bottom). Production drawdown compacts the near-well chalk (A), stretching the overburden above (B). A stress arch forms, shifting support forthe weight of shallower overburden laterally (C), resulting in a compression of the overburden and formation far from the wellbore (D). The coupled modelshows that the compressed chalk (E) cannot drain to the wellbore quickly because of low chalk permeability (F). As a result, the overpressure in the porefluid supports part of the stress-arch load. Uncoupled models do not treat these events as simultaneous, and so miss the interaction of stress arching andpore-pressure transfer. Stress arching like this has been seen in the field. Seismic images from the field show differences between a life of field seismic(LoFS) survey taken before production began and four months (top center) and six months (top right) after it began in a horizontal well (white circle) withinthe productive formation (bounded by dark reflectors). The well trajectory goes into the plane of these images. Extension, associated with traveltimeincrease (orange), appears to develop within certain layers above the well. On either side of the well, a traveltime decrease (blue and dark green) aboveand below the formation may indicate compression of the side supports of a stress arch. Behavior within the formation cannot be seen in the time-lapseseismic images.

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34. Kristiansen TG and Pattillo PD: “Examples From 20 Yearsof Coupled Geomechanics and Fluid Flow Simulation atValhall,” paper P06, presented at the 12th SPE BergenOne-Day Seminar, Bergen, Norway, April 20, 2005.

35. Barkved OI, Kommedal JH, Kristiansen TG, Buer K,Kjelstadli RM, Haller N, Ackers M, Sund G and Bakke R:“Integrating Continuous 4D Seismic Data intoSubsurface Workflows,” paper C001, presented at the67th EAGE Conference and Exhibition, Madrid, Spain,June 13–16, 2005.

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Monitoring Ground LevelThe Groningen gas field lies beneath the coastalplain of The Netherlands. It has been operated byNederlandse Aardolie Maatschappij B.V. (NAM),a joint venture between Shell and ExxonMobil,since its discovery in 1959. The sandstoneformation has porosity of 10% to 20% and iscompetent, meaning that it does not experiencethe type of pore collapse that occurs in theEkofisk and Valhall fields. However, theformation is about 100 to 200 m [328 to 656 ft]thick, so even though its elastic strain is small,the total displacement of the reservoir

boundaries is not. The formation is about 3 km[9,840 ft] deep. This depth, in combination withthe reservoir’s areal extent—a diameter of about30 km [18.6 mi]—means that subsidence overthe center of the field is about the same as thereduction in formation thickness.

In the low-lying areas of The Netherlands,water management is a primary concern.Protection against water encroachment mayrequire embankment and reinforcement oflevees, building water-control structures orinstalling pump stations. NAM provides funds

when additional measures are required tocombat the consequences of gas-production-induced subsidence. Knowing the amount ofsubsidence and its eventual extent is critical forthis effort.

NAM operates several fields in this area, all ofwhich are covered by a subsidence-monitoringprogram. In addition to subsidence from thesefields, the adjoining aquifers also deplete andcompact. A series of elevation surveys hasmonitored subsidence over this area, starting in1963 (above). A contractor carries out thesurveys in accordance with Dutch government

> Compaction and subsidence measurements, and the network of monitoring stations over the Groningen field. An extensive network of surface monitoringstations (top) covers several fields (green shading), including the large Groningen field in the northeast portion of this area. A benchmark near the centerof the field (red circle) is also near a well used for compaction monitoring. Total measured subsidence (bottom left, blue) encompasses all effects,including gas production. Geodetic deformation analysis using data from all stations is required to derive subsidence induced only by gas production (red).Compaction in a nearby monitoring well (black) follows the same trend (note that the units are different). Replotting the Groningen data indicates thatcompaction increases linearly with pressure decline (bottom right).

ZUIDWENDIG OOST

USQUERT

WARFFUM

LAUWERSOOG-OOST

LAUWERSOOG-WESTLAUWERSOOG-C

MODDERGAT

NES

AMELAND-WESTGAT

AMELAND-OOST

OUDEPEKELA

KIELWINDEWEER

GRONINGEN

RODEWOLT

BEDUMFEERWERD

LEENS

SAAKSUM WEST

MUNNEKEZIJL

KOLLUMERLAND

EZUMAZIJL

KOLLUMKOLLUM NOORD

ENGWIERUM

ANJUM

OOSTRUM

BLIJA-ZUID OOSTBLIJAFERWERDERADEEL

RODEN

NORG

PASOP

EEN

ZEVENHUIZEN

BOERAKKER

MOLENPOLDER

SEBALDEBUREN

GRIJPSKERK

MARUMERLAGE

DONKERBROEK

GROOTEGAST

SURHUISTERVEEN

MARUM

URETERP

TIETJERKSTERADEELSUAWOUDE

BLIJHAMANNERVEEN

ASSEN

ELEVELDAPPELSCHA

VIERHUIZEN-OOST

VIERHUIZEN-WEST

KOMMERZIJL

VRIES ZUID

VRIES CENTRAAL

VRIES NOORD

NORG ZUID

OPENDEOOST

SAAKSUM OOST

Winschoten

ASSEN

VEENDAM

HEERENVEEN

DRACHTEN

Leek

GRONINGEN

Sappemeer

Delfzijl

LEEUWARDEN

Dokkum

251960 1970 1980

Year

Subs

iden

ce, c

m

Com

pact

ion,

mill

istra

in

1990 2000

20

15

10

5

0

1.0

0.8

0.6

0.4

0.2

0.0

Total subsidence

1984

1986

1993

1997

20052000

Induced subsidence

Compaction (millistrain)

1.0250

Reservoir pressure, bar

Com

pact

ion,

mill

istra

in

100150200

0.0

0.2

0.4

0.6

0.8

0

0 6 miles

10 km

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guidelines. The leveling surveys measure thetotal subsidence, and geodetic deformationanalysis using data from all stations is requiredto determine the subsidence induced by gas production.

Other monitoring takes place in wells in thefields. Radioactive bullets indicate formationcompaction in several wells, and there are alsoseveral locations for monitoring the compactionof surface sediments. The radioactive bulletlocations are monitored every five years using theFormation Subsidence Monitoring Tool (FSMT).Since monitoring began in 1983, formationcompaction has increased linearly with pressure decline.

Shallow compaction is monitored in wellsabout 400 m [1,312 ft] deep, by accuratelymeasuring the change in distance from surface tothe bottom of the well. Measurements overGroningen field were made from 1970 through2003 in 14 shallow wells. These observations haveresulted in reliable trends, but those trends arelocation-specific and cannot be extrapolatedareally. The shallow compaction-monitoringprogram over Groningen has been discontinued,but it is continuing over some outlying fieldswhere monitoring began only in 1992.

The results of surface-subsidence andformation-compaction measurements are incorpo -rated into a geomechanical model that is looselycoupled to a reservoir flow model. Resultsindicate that the maximum subsidence overGroningen in 2003 was about 24.5 cm [9.65 in.].

NAM also forecasts subsidence to the year2050 and, at a 95% reliability interval, predicts asubsidence bowl with a maximum depth between

38 and 48 cm [15 and 19 in.], and a mostprobable value of 42 cm [16.5 in.]. The predictioncompleted in December 2005 is not very differentfrom the 2000 prediction, with discrepanciesmostly in the aquifer areas where well control isnot available.

Prior to production of hydrocarbons fromthese fields, this part of The Netherlands had hadno recorded seismic activity. Since 1986, therehave been several light tremors, some causingminor damage to property. NAM beganmonitoring seismicity and settled claims withproperty owners. The Netherlands established anew mining law in 2004 that outlined a formalclaims procedure.

Looking to the future, NAM has investigatedthe use of InSAR with permanent scatterers (PS)over Groningen field. In close cooperation withDelft University of Technology, NAM investigatedthe PS-InSAR technique for the Groningen field with a total of 104 interferograms obtainedin the period 1993 to 2003 from the satellitesERS1 and ERS2. About two-thirds of thosemeasurements were obtained while the satellitewas descending toward the horizon. The PSdensity over the field is lower than in an urbanenvironment, but there are enough scatterers to

provide sufficient spatial coverage of thesubsidence bowl (above).36

Although the PS-InSAR results reflect theapproximate shape and degree of subsidence asdetermined by the leveling survey, there werediscrepancies between the ascending anddescending measurements. NAM continues toevaluate this technology, but more analyticalunderstanding is needed before relying on thismethod for the Groningen field. Other companiesare studying its use elsewhere, such as overdiatomite fields in California.

Some fields in the extended Groningen areaare not yet in production, pending approval of aproduction plan that incorporates subsidencemonitoring and control. As an example of theextent of these plans, some small fields underlieenvironmentally sensitive tidal flats. Theproposed plan calls for tempering production toa rate that matches the natural rate ofsedimentation in the tidal areas. Thus, althoughthe producing formation will compact, the birdfeeding grounds in the tidal flats will remain atthe same level. Clearly, this is an example of acompany working to minimize the impact ofcompaction and subsidence on the environment.

64 Oilfield Review

36. Ketelaar G, van Leijen F, Marinkovic P and Hanssen R:“On the Use of Point Target Characteristics in theEstimation of Low Subsidence Rates Due to GasExtraction in Groningen, The Netherlands,” presented at FRINGE05, the Fourth International Workshop onERS/Envisat SAR Interferometry, Frascati, Italy,November 28–December 2, 2005.

37. Li X, Mitchum FL, Bruno M, Pattillo PD and Willson SM:“Compaction, Subsidence, and Associated CasingDamage and Well Failure Assessment for the Gulf ofMexico Shelf Matagorda Island 623 Field,” paper SPE 84553, presented at the SPE Annual TechnicalConference and Exhibition, Denver, October 5–8, 2003.

38. For more on sustained casing pressure: Abbas R,Cunningham E, Munk T, Bjelland B, Chukwueke V,Ferri A, Garrison G, Hollies D, Labat C and Moussa O:“Solutions for Long-Term Zonal Isolation,” OilfieldReview 14, no. 3 (Autumn 2002): 16–29.Brufatto C, Cochran J, Conn L, Power D, El-Zeghaty SZAA, Fraboulet B, Griffin T, James S, Munk T, Justus F, Levine JR, Montgomery C, Murphy D,Pfeiffer J, Pornpoch T and Rishmani L: “From Mud toCement—Building Gas Wells,” Oilfield Review 15, no. 3(Autumn 2003): 62–76.

> PS-InSAR measurement of the Groningen field. The extent of the Groningen field—yellow and redcolors in the upper right of this map—is apparent in the measurement of permanent scatterers (PS)from a satellite InSAR measurement (in descent). The maximum subsidence rate over the center ofthe Groningen field is about 8 mm/yr [0.3 in./yr] averaged over the period from 1993 to 2003.

50 k

m

85 km

–8 mm/yr subsidence

–8 to –7 mm/yr

–7 to –6 mm/yr

–6 to –5 mm/yr

–5 to –4 mm/yr

–4 to –3 mm/yr

–3 to –2 mm/yr

–2 to –1 mm/yr

–1 to 0 mm/yr

0 to 1 mm/yr

1 to 2 mm/yr

2 mm/yr uplift

10 km

6 miles

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Autumn 2006 65

Mitigating Compaction-Induced Damage in the Gulf of MexicoProblems with compaction have also occurred inthe Gulf of Mexico. The Matagorda Island Block623 field on the continental shelf experiencedwell failure or casing damage in all 17 devel -opment wells producing from the main reservoirduring the past 16 years of production.37 The wellfailures involved sand production and sustainedcasing pressure, and the casing damage in bothreservoir and overburden sections includedcasing offset, tight spots and parted or collapsed

casing.38 Operator BP, formerly Amoco,performed a comprehensive analysis to deter -mine the root cause and provide practical adviceto apply to replacement wells.

This gas field with 3 Tcf [85 billion m3] ofreserves comprises a stacked series of highlyoverpressured sands and sits at depths between9,000 and 13,500 ft [2,743 and 4,115 m] subsea.The overburden is also highly overpressured upto a depth of about 8,500 ft [2,590 m] subsea. Themain reservoir, the Siph (D) 120/122 with a gross-pay thickness of 500 ft [152 m], had an initialformation pressure of 12,000 psi [82.7 MPa] at13,100 ft [3,993 m] subsea.

The formation rock is poorly consolidated towell-cemented, fine-grained sandstone, withporosity ranging from 20 to 32%, andpermeability from 10 to 2,843 mD. The pore-volume compressibility is a function of rock typeand stage of depletion and varies from 4 x 10-6 to17 x 10-6/psi [6 x 10-4 to 25 x 10-4/kPa]. As of April2006, the reservoir had been depleted to a levelof 1,417 psi [9.77 MPa]. From 1986 to 2000, themaximum reservoir compaction was 5.32 ft[1.62 m], with a subsidence bowl 1 ft [0.3 m]deep (above).

> Compaction and subsidence in the Matagorda Island Block 623 field. The maximum formation compaction for the Siph (D)120/122 reservoir is about 5.32 ft [1.62 m] (top left), with lateral movement toward the center of the field (bottom left and right).The mudline subsidence, centered over the field, has a maximum of 1 ft [0.3 m] (top right).

Layercompaction, ft

5.32

Layer east-westdisplacement, ft

3.43

1.72

0

–1.88

Layer north-southdisplacement, ft

2.25

0

–2.22

–4.01

2.52

0

–1.22

Y

X

10,000 ft

10,0

00 ft

Y

X

10,000 ft

10,0

00 ft

Y

X

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00 ft

Y

X

10,000 ft

10,0

00 ft

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0.59

1.02

0.71

0.40

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3.5 ft

2.25

ft4.

0 ft

1.9 ft

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Development occurred in three phases.Phase I wells were drilled between 1982 and1989. Phase II wells were drilled between 1995and 2001 (left). Failure in both phases occurredat about 2 to 3% compaction strain. Phase IIIwells were drilled after the root-cause study ofthe earlier well failures.

Sustained casing pressure in Phase I wellstypically occurred about six months after asignificant increase in sand production. Most ofthe Phase I failures in the overburden occurrednear the top of the reservoir; none wereassociated with known faults. Wells failed after10 to 13 years of production.

Casing damage in Phase II began muchearlier in well life, after one to five years ofproduction, and had a high correlation withmajor fault location. No sand production hadbeen observed up to the time of the evaluation in2001, but all wells developed sustained casingpressure. In addition to a much higher rate ofproduction in Phase II wells, they were allcompleted as frac packs; Phase I wells had avariety of completion techniques, but none werefrac packed.39

Operator BP conducted an evaluation of thefailure modes using reservoir and well modelsand the geomechanical behavior of the formationand overburden. In the center of the field,formation compaction resulted in enough casingstrain to cause failure (next page, left). Anothergeomechanical model examined fault andbedding-plane movement. It indicated that thefaults would not become reactivated untildepletion had reached about 9,000 psi [62 MPa],which occurred about one year after thecompletion of the Phase II drilling program. Thisresult explains why no Phase I well failures wereattributable to fault movement.40

Two completion methods used in this fieldwere also modeled. Well orientation ranged fromvertical to horizontal. A connection typical ofcasing and liner overlap in the overburden inPhase II wells was modeled, and it indicated thata vertically oriented well can accommodate onlyabout 2% compaction in the surroundingformation before reaching a 10% plastic strain,the design limit for the casing. In contrast, themodel showed that a horizontal well canaccommodate almost 8% formation compactionbefore reaching the design limit.41

The second completion model examined afrac-pack assembly, also typical of Phase II wells.Again, a horizontal wellbore can accommodatemore strain, 12% as opposed to 3% for a verticalorientation, before reaching the 10% design limit(next page, right).

66 Oilfield Review

>Well-failure history in the Siph (D) 120/122 formation. Phase I drilling occurred between 1982 and 1989,and Phase II drilling lasted from 1995 until 2001 (red triangles on axis, top). The first Phase I well failed in1994, and the last one failed in 2001. Phase II wells failed more quickly. The pressure decline (points) wasroughly linear with time. The formation had a high compaction rate (purple) early and late in field life, witha reduced rate in between. An analysis (bottom) showed that Phase I wells suffered sand production(light blue) before experiencing sustained casing pressure (green). The height of the bar is the length ofwell life before onset of the problem. The Phase II wells had shorter lives and no sand production. Thepeak (red) and constant (blue) well rates were significantly higher for Phase II wells.

Botto

mho

le p

ress

ure,

psi

12,000

11,000

10,000

9,000

8,000

7,000

6,000

5,000

4,000

3,000

2,000

1,000

01982 1984 1986 1988 1990 1992

Year1994 1996 1998 2000 2002

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pact

ion

stra

in, %

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5

4

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0

Wel

l life

, yea

rs

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

C-6E-1 C-4 635-1C-2 C-1 E-2C-3 D-1 C-2stC-5 D-2 C-8 D-3C-7Well name

Peak production rate

Sustained production rate Gas

rate

, MM

cf/d

80

0

10

20

30

40

50

60

70

CHGP CHGP CP CP FPCP

CHGP: Cased-hole gravel packCP: Cased and perforatedFP: Cased hole frac pack

Sand productionCasing pressure

Phase I drilling

Phase II drilling

Failures

Failures

Initialcompaction

rate

Reducedcompaction

rate

Bottomhole pressure

Compaction strain

Acceleratedcompaction

rate

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Autumn 2006 67

The evaluation indicated that three of fivekey Phase II wells would experience the 2 to 3%compaction strain before the end of the field life,so replacement wells would be necessary. A thirdphase of drilling has begun, but only about1,800 psi [12.4 MPa] of depletion is left beforeabandonment, resulting in less than 1.5%additional compaction strain. This is insufficientto cause the completion to fail in the formation.However, the reactivated faults in the over -burden will continue to move and potentiallyshear the casing.

Phase III wells were designed to counteractthe fault-slip problem and to strengthen thepressure-seal capability of the wells; three wellshave been drilled using the improved design. In

the overpressured overburden, the annulus wasback reamed to 15 in. [38 cm] and leftuncemented to avoid the potential of shearing atreactivated faults. The 75⁄8-in. liner was tied backto the 117⁄8-in. casing shoe and cemented insidethe 97⁄8-in. casing, strengthening the well bothstructurally and hydraulically.

The Phase III wells are producing at high,stable rates, about 15 MMcf/d [425,000 m3/d] foreach well. The Matagorda Island study hasprovided BP with a methodology for other Gulf ofMexico fields. For example, the King West field,which had a much greater compressibility thanthe Matagorda Island field, was judged to be alow to moderate risk, because the expectedpressure depletion is less.42

In another Gulf of Mexico field, a 3Dmechanical earth model was developed to aiddrilling and to assess the impact of compaction onwell stability and subsidence. This deepwaterturbidite reservoir, operated by Murphy Oil,comprises interbedded sand and shale.43 Themodel showed that vertical strain could reachabout 8% in a high-porosity section of the field.Even in an area of the field with lower strain, thewell could experience casing buckling if it were

> Casing displacement and strain in a vertical well. Formation compaction ledto significant casing displacement within the Siph (D) formation (top). Thecompressive strain, ε, reached about 1.8%, with tensile lateral strains (bottom).

–500

–2,500

–4,500

–6,500

–8,500

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ubse

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ubse

a, ft

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Casing strain, %

X-displacement to the west

εzzεxx

εyy

Compression

Siph (D) perforations from 13,243to 13,409 ft TVD subsea

Tension

–6.0 –4.0 –2.0 0.0 2.0 4.0 6.0 8.0

–2.0 –1.5 –1.0 –0.5 0.0 0.5 1.0 1.5

39. For more on frac packs: Gadiyar B, Meese C, Stimatz G,Morales H, Piedras J, Profinet J and Watson G:“Optimizing Frac Packs,” Oilfield Review 16, no. 3(Autumn 2004): 18–29.

40. Li et al, reference 37.41. Li et al, reference 37.42. Li X, Tinker SJ, Bruno M and Willson SM: “Compaction

Considerations for the Gulf of Mexico Deepwater KingWest Field Completion Design,” paper SPE/IADC 92652,presented at the SPE/IADC Drilling Conference,Amsterdam, February 23–25, 2005.

43. Sayers C, den Boer L, Lee D, Hooyman P andLawrence R: “Predicting Reservoir Compaction andCasing Deformation in Deepwater Turbidites Using a 3DMechanical Earth Model,” paper SPE 103926, presentedat the First International Oil Conference and Exhibition inMexico, Cancun, Mexico, August 31–September 2, 2006.

> Finite-element grid of a frac-pack undercompaction. Formation compaction led tolocalized buckling at the casing (blue) betweenthe screen (yellow) and the coupling (red).

Deformation

Base pipe

Deformation

Shunt tube

Shunt tube

Screen

A rings

A rings

Gravel

Casing

Screen

Coupling

Base pipe

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unsupported by cement and formation (above).This showed the importance of drilling an in-gauge borehole with casing centralized, having agood-quality cement job and producing in a waythat avoids sand production.

Overcoming That Sinking FeelingThe struggle to control subsidence will go on. Asthe case studies illustrate, engineers andgeoscientists continue to develop and employnew tools to understand and mitigate its effects.

Coupled flow and geomechanical simulatorsmay become powerful weapons in the struggle,but at this time they are still considered too slowfor day-to-day reservoir management. Applicationof time-lapse seismic studies to monitorcompaction across large portions of reservoirs

has made great strides over the past couple ofyears; satellite measurements have potential toprovide equally large coverage for subsidence.Waterflooding has been used to combatsubsidence for many years, but combining it withnew methods of modeling and monitoringpromises to make it a more precise and effectivemanagement practice.

Mitigating wellbore damage is at least partlyan economic issue. With enough steel in theborehole, many more wells can be protected fromcompacting, stretching, or minor movement offaults. But that protection comes at a high cost.Advances in modeling are also helping to makeintelligent completion choices.

New problems will foster new tools. The SonicScanner acoustic scanning platform providesinformation about conditions around a wellbore.44

The tool measures shear-wave anisotropy as lowas 2%. Its multiple depths of investigation can

provide a radial profile of compressional andshear behavior several feet into a formation.Application of this tool in a dynamic, compactingenvironment may hold promise for newdiscoveries, and perhaps new ways to determinegeomechanical parameters in situ.

Even though the city of Venice continues tosubside today, by understanding the effects ofwater and gas extraction and shutting in thosewells, planners brought the effects of man-made subsidence under control, dramaticallyslowing the rate at which the city sinks.Modeling, monitoring and logging reduceuncertainties relating to compaction of areservoir, allowing companies to mitigate itseffect in oil and gas fields. However, as in Venice, the struggle between nature andtechnology continues. —MAA

68 Oilfield Review

44. Arroyo Franco JL, Mercado Ortiz MA, De GS, Renlie Land Williams S: “Sonic Investigations In and Around theBorehole,” Oilfield Review 18, no. 1 (Spring 2006): 14–33.

> Formation and casing strain in a Gulf of Mexico turbidite field. The mechanical earth model indicates that the verticalstrain in the formation may reach 8% (yellow and orange shades) in the part of the field that has the highest porosity(top left). Along a proposed well path near that high-porosity area, the compressive strain on casing exceeds 4% in thesand formations, with a tensile strain up to 1% in the interbedded shales (graph). These values are lower than thevertical formation strain because the well is deviated, but that deviation also introduces shear stresses to the casing.Four cases are identified in the table: two types of casing were analyzed, each for two values of formation Young’smodulus. For the four cases, unsupported casing buckles when casing strain is less than 1% (right on graph). However,if it is supported by cement and formation, the casing can withstand compressive strain of 6% or more before buckling(left on graph), which indicates the predicted strains on casing are within acceptable limits if the casing is supported.

–10 –8

1 1,2 3,43

Supported

Unsupported

2 4

–6 –4Casing axial strain, %

True

ver

tical

dep

th

–2 0 2

Case Casing diameterand weight

Young’s modulusof formation, psi

1

2

3

4

9 7⁄8-in. 62.8 lbm/ft

9 7⁄8-in. 62.8 lbm/ft

7 3⁄4-in. 46.1 lbm/ft

7 3⁄4-in. 46.1 lbm/ft

147,000

88,300

147,000

88,300

-0.1

Vertical strain

9% 6% 3% 0%

-0.075 -0.05 -0.025

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