Te Depth-Area-Tickness (DA) Method or Calculating Ca lculating Gross Rock Volume: A Better Way to Model Hydrocarbon Contact Uncertainty
Bill James1 (retired), Allen . Grundy 2 (retired) & Mark A. Sykes3 1
ExxonMobil Upstream Research Co., 3120 Buffalo Speedway, Houston, X 77098-1806, USA 2 ExxonMobil Development Co., 12450 Greenspoint Drive, Houston, X 77060-1916, USA 3 ExxonMobil ExxonMobil Exploration Co., 222 Benmar Drive, Houston, X 77060-2502, USA
Gross Rock Volume (GRV), the volume o rock between a top and base reservoir surace and above a known or postulated hydrocarbonwater contact in a geologic trap, is ofen the most influential parameter in determining the magnitude o resource volumes contained, or potentially contained, in that trap. In any petroleum volumetric analysis it is thereore essential to calculate both the best estimate and the range o uncertainty or GRV accurately and appropriately. However, However, geologic geologic traps exhibit exhibit highly variable and ofen ofen complex geometries. Tey range in shape rom simple anticlines, resembling an upturned bowl, to all manner o intricately structured eatures with variable flank dip, overturned overturned limbs and multiple multiple culminations. culminations. Tere is thus a need or a single and reliable equation that can calculate GRV or this diverse suite o trap configurations. Direct input o o a GRV range, range, or example example calculated in a mapping mapping tool as a result o combining explicit choices o closure area, reservoir thickness and hydrocarbon contact depth assumptions, should be avoided. Tis is because the GRV o a trap, and its range o uncertainty uncer tainty,, is a product o the interaction between these three largely independent variables. Attempts Attempts to short-cut directly to low, low, base and high case GRV values in this this manner will inevitably inevitably introduce introduce bias into the estimation estimation process.
Several methods have been developed over the years to estimate GRV on a screening basis. Tese requently involve conflation o the trap’s area o closure, the hydrocarbon column height, estimated reservoir thickness and a wedge correction or geometry actor. Whilst these methods are stable, and quick to use, or all but the most simple traps they provide only a rough estimate o GRV. Te depth-area-thickness (DA) (DA) method o calculating GRV provides greater accuracy and flexibility in calculating GRV and its range o uncertainty. Tis is because it allows hydrocarbon contact elevation ranges, and closure area and reservoir thickness uncertainties to be modeled independently. independently. Te DA DA method achieves this this by defining a mathematical abstraction o the trap geometry in area-depth space into which an contact elevation or range can be convolved and modeled. Tis allows or a rapid GRV calculation, that can be used in a Monte Monte Carlo simulation, in order to establish an unbiased estimated range o GRV. Te DA DA methods requires that the geologist geologist generate generate an table o depth-area-thickness values or a selection s election o contours along the flanks o the trap. Tis table o values can be calculated by hand, or in a geologic mapping application by using either standard unctions or bespoke workflows or macros.
SECION 1: GROSS ROCK VOLUME VOLUME AND IS CONROLS C ONROLS .1
Fig. 1a: BetaProspect: Map
Fig. 1b: RockVolume Definitions
Fig. 1c: GRV Uncertainty Controls: 1 –Structural Dip –
.
.1
Fig. 1d: GRV Uncertainty Controls: 1 –Structural Dip –
.
Fig. 1e: GRV Uncertainty Controls: 2 –ReservoirTickness – T
.
Fig. 1: GRV Uncertainty Controls: 2–Reservoir Tickness .1
5.5
– 3
(GrossRockVolume) :5
=the rock volumebetween upperand lowerdefined surfaces abovea depth ofinterest. =
(GrossTrapVolume) –
4.5
Thin Basecase
4
(WasteRockVolume)
Thick ) 3 3.5 m k ( V R G 3
GTV
Crest= 1306m GRV
R e s e r v r o a i n r g t e h i c k n e s s
2.5
2
) 3 m k ( 1.5 V R G
Hydrocarboncontact
Hydrocarboncontact 2.5
WRV
1 2
GRVshallow dip > GRV base
Hydrocarbon-WaterContact (HCWC)
Spill = 1372m
casedip>
GRVthick reservoir > GRVbase case reservoirthickness> GRVthin reservoir
GRVsteep dip 1.5
5km
0.5
1 0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1. 4
1. 5
0
Structuraldip(degrees)
Contourincrement= 6m
0
10
20
30
40
50
60
ReservoirThickness(m)
Fig. 1a
Fig. 1b
Fig. 1c
Fig. 1d
Fig. 1e
Fig. 1
Troughout thisposter, thedepth-area-thickness(DA)concept orcalculatinggross-rockvolume (GRV) willbeillustrated usinga simpleanticlinal prospect called “Beta”. TeBeta prospect’screst islocated at a depth o1306m. Tereis a spillpoint to thesouth-west othestructure at adepth o1372m. Teclosureheight otheBeta structureisthus 66m. totassimusapero dit quisaut inihilisinimharum acea conemut aboribus.
GRVisdefined asthe volumeorock between thetopand baseoa reservoirabovea depth ointerest,such asa hydrocarbon rbon contact. tI ismathematically quivalent q e uivalent totheGross rapVolume(GV) –the entirevolumeo thestructure below thetop reservoir-minus theWasteRock Volume(WRV) -the volumeo non-reservoirrocklying between thebase othe reservoir and thedepth ointerest.
GRVisa unction othree independent geologicvariables–structuraldip, reservoirthickness, and hydrocarbon contact depth. Itsuncertainty ishencea unction otheun certainty in thesethreevariables. Testructuraldipo theflanko a structuredip may beuncertain astheresult o lessthan perect seismicdata quality, orissuesaround theprocesso depth-conversion. Given a fixed hydrocarbon contact elevation, a hallow hs allow flankdipwill yield a largerprospect GRVthan a steepflank dip.
Terelationshipbetween flankstructural dipand prospect GRVisnon-linear. Forevery increment instructuraldipdecrease (flattening), theincremental increasein GRVbecomesmore significant. Tisis becauseclosure area increasesmuch more quickly perunit dipincrement at low dipthan it decreasesat high dip.
Reservoirthicknessexertsan obviousinfluence on prospect GRV. Given a constant hydrocarbon contact and flankdip, a thicker reservoirwillyield a greaterGRVthan a thinnerreservoir.
Terelationshipbetween reservoirthickness and prospect GRVisalso non-linear. However, in contrast to structuraldip, as reservoirthicknessincreasesits positiveinfluenceon GRVwanes. Tisisbecause, asthereservoirthickens, it displaceswaste placeswaste rockin thecoreot hestructurebelow thedepth ointerest. However, thevolumeothisdisplaced non-reservoirprogressively decreasesasoreach increment in reservoirthickness.
.
Fig. 1g: GRV Uncertainty Controls: 3–Hydrocarbon Contact Elevation –
Fig. 1h: GRV Uncertainty Controls: 3 –Hydrocarbon ContactElevation .1
Fig. 1i: GRV Uncertainty Controls: Convolved Model .1
–
Fig. 1j: BetaProspect: Lines o Cross-section -
.1
Fig. 1k: BetaProspect: Cross-section A-A’ -
.1
Fig. 1l: BetaProspect: Cross-section B-B’ .
-
-
3 A’
2.5
B Shallow
A
Hydrocarbon-contact depthrange
Spill-point
B’
B
A’
Crest=1306m
Crest=1306m
2
Intermediate
) 3 m k 1.5 ( V R G
Crest=1306m
Spill (outofplane) =1372m
Spill =1372m
→ ƒ
Deep 1
Vertical and horizontal scalesin meters
B’
GRVshallow contact > GRVintermediatecontact > GRVdeep contact
0.5
Vertical and horizontal scalesin meters
5km
Spill = 1372m -1306
-1312
-1318
-1324
-1330
-1336
-1342
-1348
-1354
-1360
0 -1372
-1366
A
Contourincrement= 6m
HCWC(m)
Fig. 1g
Fig. 1h
Fig. 1i
Fig. 1j
Fig. 1k
Fig. 1l
Hydrocarbon contact depth also exertsan obviousinfluenceon prospect GRV. Given constant structuraldip and reservoir thickness, a deeperhydrocarbon contact willyield a greaterGRVthan a shallow one.
Terelationshipbetween hydrocarbon contact depth and prospect GRVisagain non-linear. Asa contact becomesdeeper, there isan inordinateincreasein theincrementally added GRV.Tisisas a result othenon-linearrelationshipbetween thearea and volumeoa cone. Forevery increment in contact depth, theassociated increasein area adds morevolumethan the previous area increment. Unlikereservoirthickness, theinfluenceothe hydrocarbon contact depth isnot tempered by any effect othe corevolumeo wasterock.
By convolvingthethree independent uncertaintieswhich controlprospect GRV-structural dip, eservoirthickness, erservoirthickness, and hydrocarbon contactdepth, a esultingtrend ersultingtrend in GRVuncertainty asunction o thethree variablescan beresolved. It is highly asymmetricunction. SmallGRVoutcomesare armoreabundant than largeGRV outcomes. Tisis becauseallthree independent variablesmust beavorableto yield a high GRV , whereasonly oneothe threevariablesbeingunavorablecan yield a lowGRV,regardlessothe magnitudeothe othertwo.
Troughout thisposter, two linesocross-section, A-A’and B-B’, willbeused to illustratethe geometry otheBeta prospect. Te A-A’section runsSW-NE, alongthestrikeothe structure, andpassesthrough thespillpoint to thesouth-west otheanticline. TeB-B’dip section runsNW-SE acrosstheanticline.
Cross-section A-A’clearly showsthegeometry otheBeta prospect anticline, with a crest at 1306m, a closureheight o 66m, and a spillpoint to thesouth-west at a depth o1372m.
Cross-sectionB-B’doesnot passthrough thespill point, butitsintersection againstthetopo thereservoirin thisdip section can beseen.
SECION 2: AV AVAILABLE AIL ABLE GRV-CALC GRV-CALCULAION ULAION MEHODS .
Fig. 2a: Available GRV ModelingMethods
Fig. and Wedge (Geometric)Correction . 2b: Area o Closure, , ReservoirTickness T
Fig. 2c: Area o Closure, ReservoirTickness and Wedge (Geometric)Correction .
,
Fig.2d: rapezoidalEquations .
T
MANUAL
T A1
anticline
flat-topped dome
L/W=>10
L/W=1
flat-topped anticline
A0
dome
1. Areaofclosure,
Reservoirthick v oirthicknessandWedge(Geometric)correct i c)correction. i on.
Trap area
2. Trapezoidal equationsusing area datafrom aseries ofcontours.
Waste crest
L/W=2-10
L/W=2-10
conicalslice
L/W>=10
L/W=1
contours
h
>=1
reservoir thickness
conicalslice
3. Graphicalmethod – cross-plotof depthand area.
t h g i e0.8 h n m u l o C0.6 / s s e n k c0.4 i h t r i o v r e s0.2 e R
column height
DIGITAL 4. Directgrid-based calculation frommapping software. wedge
5. Depth-area-thickness – thesubjectofthisposter.
trapezoidalslices trapezoidal slices HCWC
CONE:
V = ⅓Ah
TRAPEZOID:
0
0.2
0.4
0.6
0.8
V = ½(An+1+An )h
TheGRV isthesum ofthe conical slice+ all thetrapezoidal slicesminusthe equivalentvolumeforthe wasterock.
WedgeCorrection
0
1
Fig. 2a
Fig. 2b
Fig. 2c
Fig. 2d
SeveralGRV-calculation methodologieshavebeen developed by thepetroleum industry overthelast century. Tesewill each bebriefly reviewed. However, therecently-invented Depth-Area-Tickness(DA)method isthesubject o thisposter. It isa quickca lculation which rendersit tractablewhen used in association with a MonteCarlo simulator. Tistechnique probabilistically calculatesthe volumetricrange oa prospect romthedefined uncertaintiesin structuraldip, reservoir thickness, and hydrocarbon contact elevation.
Tesimplest method orcalculatingGRVis to measurethearea oclosure, thereser voirthickness, and thecolumnheight othe structureand calculatethe volumedirectly, correctingor thewedgeat theedge othe structure.
A nomograph hasbeen developed to correct ortheoverestimate in GRVcaused by thewedge, asunction othe ratio o reservoirthickness to column height ht and thegeometry othestructure.
A moresophisticated approach isto measurethe area oclosureat a seriesodepths (contours) down thestructureand calculatethe volumeo rockcontained in each slicethusdefined. Equationsovolumeor a trapezoidand a conearethe only math required. Teindividualslice volumescan then besummed to calculatethetotal prospect volume. Wasterock volume(WRV) must becalculated in thesame way and subtracted romthetr apvolume(GV) to yield theGRV.
Fig. 2e: Graphical Method
Fig. 2: MappingSofware
Fig. 2g: Comparison o GRV-calculation methods .
.
.
-
subjectcell 3.5 Single-square calibration
-1300
3
.1
-1310
0.1km
.6
-1320 -1330 -1340 ) -1350 m ( h t -1360 p e d
3.0
3 GascapGRV=3.2squares=0.32km
1
.5
.4
.4
2.5 .2
)
GOC
.6
.6
.5
.2
1
1
1
.9
.5
.1
.7
1
1
1
1
.9
.4
.1
.2
.8
1
1
1
1
1
.9
.1
.2
.2
.2
-1370
3
m k ( 2.0 V R G
3 OillegGRV=22.0squares=2.20km
.2
.2
1.5
.6
.2
.2
.2
.2
1.0
.1
HCWC -1380 Reservoirthickness
-1390 -1400
0.5
3
1 9
-1420 0
10
20
30
40
50
60
70
80
90
100
2
110
area (km2 )
ATWC TrapezoidalEquations Graphical
0.0
8
TotalGRV =25.20 squares =2.52km3
-1410
Integrationofsubject-cell volumebetweenfittedtop surfaceandbase-plane
6
15
30
Mappingsoftware 45
66
….. ontothe nextcell.
Fig. 2e
Fig. 2
Fig. 2g
Tegraphicalmethod a lmethod isintuitiveand e and hastheadvantageo e o beingableto calculateGRVorreservoirsonon-uniorm thickness. Again,areasare required ora seriesocontoursdown thestructure. Reservoirthicknessesat thoseelevationsare then projected down onthegraph to plot correspondingdepth-area pointson thebasereservoir surace. GRVisrepresented by thearea between thecurves, abovethe depth othehydrocarbon contact. It can bemeasured by countingand summing thesquares which fillthis area, afercalibratingthe area oa singlesquare with a sub-suracevolume by multiplyingone x-axisincrement by oney-axisincrement.
Most mappingsofware relieson summingthevolume oea ch grid cellbetween thetop reservoir suraceand a baseplane, typicallya hydrocarbon contact. Tistypically involvesdevelopinga fitted suraceacrossthe topo each grid cellby integratingthetopology othecell in questionwith itsneighbors. Teprogramsperormthisoperation oreach cellwithin closureorwithin a specified boundingpolygon.
Alltheexisting methodsproduceclosely comparableGRVresultsor theBeta prospect ata varietyoreservoir thicknesses.
Te Depth-Area-Tickness (DA) Method or Calculating Gross Rock Volume:
A Better Way to Model Hydrocarbon Contact Uncertainty
SECION 4: HE DA HICKNESS CALCULAION (continued) Fig. 4i: DA Reservoir Tickness Calculations Mechanics - 8 Fig. 4i: DAT Reservoir Thickness Calculations Mechanics - 8
1100
1200
Fig. 4j: DA Reservoir Tickness Calculations Mechanics - 9
Depth
TopArea
TopThick
1100
0
100
1200
11
115
1300
38
230
1400
69
260
1500
74
180
1600
80
90
1700
88
30
g. 4j: DAT Reservoir Thickness lculations Mechanics - 9
1100
1200 140
1300
1300
1400
1400
Fig. 4k: DA Reservoir Tickness Calculations Mechanics - 10
D e pt h
T o pA r ea
T op T h ic k
1100
0
100
1200
11
115
1300
38
230
1400
69
260
1500
74
180
1600
80
90
1700
88
30
Fig. 4k: DAT Reservoir Thickness Calculations Mechanics - 10
1100
1200
D e pt h
T op A r ea
T op T h ci k
1100
0
100
1200
11
115
1300
38
230
1400
69
260
1500
74
180
1600
80
90
1700
88
30
1300 120 210 1400 280
Depth 1500
1600
1700
BaseArea 1500
Depth
BaseArea
1200
0
1300
6
1500
1200
0
1300
6
1400
32
1400
32
1500
36
1500
36
1600
41
1600
41
1700
83
1700
83
0
1600
1700
10
20
30
40
50
60
70
80
0
1600
50 1700
10
20
30
40
50
60
70
Depth
BaseArea
1200
0
1300
6
1400
32
1500
36
1600
41
1700
83
0
80
10
20
30
40
50
60
70
80
Fig. 4i
Fig. 4j
Fig. 4k
However,theDAtable can berefined and expanded by usingthed epth-area pointsexplicitly derivedon thebasereservoirsurace in step2.
In a similarashion in which thedepth-area pointson thetopsurace wereextrapolated down on to thebasereservoirsuraceto determine“top down”reservoirthicknesses, thereverseoperation can now beperormed with ht epoints explicitly calculated on thebasereservoirsurace. Tethicknessabove thesepointscan be derived by “bottomup” projection and interpolation onto thetopreservoirsurace.
Tese“bottomup”interpolations producenew, additionalpointson thetopreservoirsurace immediately abovethecorresponding basereservoirpoints, i.e. at thesamevalues orarea.
Fig. 4l: DA Reservoir Tickness Calculations Mechanics - 11 Fig. 4l: DAT Reservoir Thickness Calculations Mechanics - 11
1100 (1160, 6, 140) 1200 (1280, 32, 120) (1290, 36, 210) 1300
Fig. 4m: DA Reservoir Tickness Calculations Mechanics - 12
D e pt h
T op A r ea
T op T h ci k
1100
0
100
1200
11
115
1300
38
230
1400
69
260
1500
74
180
1600
80
90
1700
88
30
Fig. 4m: DAT Reservoir Thickness Calculations Mechanics - 12
1100
1200
(1320, 41, 280)
1300
1400
1400
1500
1600
1700
Depth
BaseArea
1200
0
1300
6
1400
32
1500
36
1600
41
1700 0
Depth
TopArea
TopThick
1100
0
100
1160
6
140
1200
11
115
1280
32
120
1290
36
210
1300
38
230
1320
41
280
1400
69
260
1500
74
180
1600
80
90
1650
83
50
1700
88
30
1500
1600 (1650, 83, 50)
83
1700
10
20
30
40
50
60
70
80
0
10
20
30
40
50
60
70
80
Fig. 4m
Fig. 4l
Te“bottomup”DA rowscan now beinterlaced into thepreliminary DAtablegenerated romthe“top down”interpolationsto completethefinal DAtable. Notethat “top down”and “bottomup”rowsdo not necessarily occurconsecutively. Each may beseparated by oneormoreothe other. Teirmutualspacingand arrangement isa unction o thedisparity in theshapeand trend o thedepth-area curveon thetop and basereservoirsuraces. However,in general, thismethod willproduceapproximately twicethenumber odata rowsthat weregenerated by thefirst pass“topdown” analysis.
Tedepth othese new pointsiseasily determined; theirarea isequal to thecorrespondingpoint on thebasesurace (seedepth-area tableon base, bottomlef), and their thicknessiscalculated by interpolation between adjacent pointson thetop reservoirdepth-area line.
SECION 5: DA CALCULAION EXAMPLES Fig. 5a: Beta Prospect – Perspective View
Fig. 5b: Beta Prospect – Uniorm Tickness Model: Perspective View
Fig. 5c: Beta Prospect – Uniorm Tickness Model: Cross-section
B
Fig. 5d: Beta Prospect – Uniorm Tickness Model: DA able
B’ Crest=1306m Reservoirthickness =45m
Spill
(out of plane)
=1372m
Vertical and horizontal scalesin meters
Line ofsection, B-B’
Legendas Fig. xx
Fig. 5a
Fig. 5b
Fig. 5c
Fig. 5d
In thissection, a seriesomaniestationsothe Beta prospect, with differentreservoirthicknessmodels, is used to illustratethe DA concept. Tisfigureexhibitsa perspectiveview othe Beta prospect structure. Similarillustrationswillhighlight each othereservoirthicknessmodelsto bedemonstrated.
Tefirst Beta prospectmodelassumes a constant reservoirthickness o45m. Tisis thesimplest othe modelspresented. Tebase reservoirsurace can beseen glowingthrough thetopreservoir surace. It hasthe samemorphology asthe topreservoir suraceas it issimply bulkshifed down by theconstant 45misochore.
A dipcross-section, ollowingthetrace oB-B’, introduced earlierin this presentation(Fig. 1j), demonstratesthe uniormthickness natu reothereservoirothismodel.
Tistable representsthe output romtheExxonMobilDA mappingmacro, mentioned in Fig. 4a. Teregularly spaced “topdown” thicknessdeterminationscan bedistinguished romtheinterlaced “bottomup”determinations. Teintroduction othe“bottomup” rowsroughly doublesthe numbero rowsin theDA tablethat would begenerated by a“topdown”only approach. Notethat the macro generatesthicknesses at orclose to thespecified valueo 45m. Tereare someminor deviationsrom theknown value, but theseare trivialin a volumetriccontext.
Fig. 5e: Beta Prospect – Uniorm Tickness Model: DA Plot
Fig. 5g: Beta Prospect – Tickening Off-structure: Perspective View
Fig. 5: Beta Prospect – Tickening Off-structure: Isochore Map
Fig. 5h: Beta Prospect – Tickening Off-structure: Cross-section
-1300.0
closing contour -1325.0
B
B
B’ Crest=1306m
Reservoirthickness =6m
-1350.0 ) m ( -1375.0 h t p e D
Spill
(out ofplane)
=1372m
Reservoirthickness =90m
-1400.0
-1425.0 B’
Vertical and horizontal scalesin meters
Line ofsection, B-B’ -1450.0 0
10
20
30
40
50
60
70
80
90
100
110
5km
Area (km2) Contourincrement= 10m
Fig. 5e
Fig. 5
TeDAplot orthe uniormthicknessreservoir modelis very simple. Tebase reservoirsurace tracksthe topreservoir suracein depth-area space.
Tesecond Beta prospectmodeleaturesa reservoirthinningoff structure. Asa result, theisochore contoursareparallelto thedepth contours. Tedepth contourcorrespondingto the spillpoint at 1372mishighlighted in green orreerence. Teminimumisochore thicknessat thecrest othe structureis 6m. Tisincreases to approximately90mat theedge othe map.
Fig. 5i: Beta Prospect – Tickening Off-structure: DA able
Fig. 5j: Beta Prospect – Tickening Off-structure: DA Plot
-1300.0
-1325.0 28 29
-1350.0 ) m ( -1375.0 h t p e D
50 52
-1400.0
-1425.0
-1450.0 0
10
20
30
40
50
60
70
80
90
100
110
Area (km2 )
Fig. 5i
Fig. 5j
TeDAtable reflectsthe thickeningoffstructure. Teisochorereservoir thicknessvaluesincreasesteadily romtheaorementioned 6mat thecrest othestructure (1306mdepth) to around 70mat thestructuralspill (1372mdepth). Notetheidentical area at thespill point, 108.7km2,to thepreviousmodel. Tisarea willbeconsistent acrossallmodelsas thestructural dipis not beingvaried between themodels, only thereservoir thickness.
TeDAplot orthe thickening offstructurereservoirmodel isairlysimpleand intuit ive.Becausetheisochorecontoursare concordant with thedepth contours, thethickeningis reflected verbatimin depth-area space. wo exampleseach o“top down”and “bottomup”thicknessdetermination arehighlighted and can becompared with theDAtablein the previousfigure (bluecircles).
Fig. 5g
Fig. 5h
In perspectiveview, thebasereservoir suracecan beseen divingoff on theflanks othe structure, beneath thetop reservoirsurace, in responseto thethickeningoff structure.
TeB-B’ dipcross-section clearly showsthe thickeningothe reservoiroff structure.
