Use of Analytical Models in Prospect Evaluation of Gas ...hydrates/MehranPresentation.pdf · A...

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Use of Analytical Models in Use of Analytical Models in Prospect Evaluation of Gas Prospect Evaluation of Gas

Hydrate ReservoirsHydrate Reservoirs

Mehran Pooladi-Darvish

Hart Conference – Commercialization of Gas Hydrates

December 5, 2006, Houston

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Prospect Evaluation:Prospect Evaluation:Realm of High UncertaintyRealm of High Uncertainty

Cumulative ProductionCumulative Production

Exploration/Exploration/Prospect EvaluationProspect Evaluation

TimeTimeReco

vera

ble

Rese

rve

Reco

vera

ble

Rese

rve

DevelopmentDevelopment OptimizationOptimization

Range of UncertaintyRange of Uncertainty

Limited DataLimited Data

Need for large number of runs Need for large number of runs and risk analysisand risk analysis

→→ Analytical ModelsAnalytical Models

3

ObjectivesObjectives

For a hydrate reservoir with underlying free gasFor a hydrate reservoir with underlying free gas

TARN

EILEEN

Gas HydrateFree GasOil

Hydrate

Hydrate/water

Gas/Water

Develop, validate and use analytical models for Develop, validate and use analytical models for quantifying ofquantifying of

The upside in gas recovery associated with the The upside in gas recovery associated with the hydrates (forward model)hydrates (forward model)

Hydrate reserve (backward model)Hydrate reserve (backward model)

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Production by DepressurizationProduction by Depressurization

Hydrate

Simplest: Simplest: Produce from the gasProduce from the gas

Hydrate/water

Gas/Water

Least energy intensive: Least energy intensive: No external heating agentNo external heating agent

Examples: Examples: MessoyakhaMessoyakha, Alaska, Mackenzie Delta, Alaska, Mackenzie Delta

Not a proven technology yet: Not a proven technology yet: Use mathematical models!!Use mathematical models!!

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Depressurization MechanismsDepressurization MechanismsDecomposition rate is controlled by our ability toDecomposition rate is controlled by our ability to

1.1. Provide heat of decomposition: 11,000 BTU/ftProvide heat of decomposition: 11,000 BTU/ft33 hydratehydrate

300

350

400

450

500

550

600

650

700

30 32 34 36 38 40 42 44Temperature (F)

Pres

sure

(psi

a)

Hydrate:Hydrate: SSHHφφRock and water: (1Rock and water: (1--φφ)+ )+ SSWWφφ

Ste=Ste=ρρccppΔΔT/T/ρρHHSSHHφΔφΔHH

Ste=0.1 Ste=0.1 –– 0.450.45RRHH=10% to 45%=10% to 45%

1 ft3 → 160 SCF(2500 psia, equivalent)

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Provide heat of decomposition: 11,000 BTU/ftProvide heat of decomposition: 11,000 BTU/ft33 hydratehydrate

From surrounding rockFrom surrounding rock

CAP ROCK

HYDRATE ZONE

FREE GAS ZONE

EA

RTH

TE

MP

ER

AT

UR

E

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2.2. Reduce the pressure within the hydrate zoneReduce the pressure within the hydrate zone

ti c

ktrφμ948

=

φ = 30%

μ= 0.02 cp

ct= 1×10–3 psi–1

K = 10 mD

φ = 30%

μ= 1 cp

ct= 1×10–5 psi–1

K(SH) = 0.01 mD

0

200

400

600

800

1000

1200

0 5 10 15 20 25 30

Time (days)

r i (f

t)05

101520253035404550

0 5 10 15 20 25 30

Time (days)

r i (f

t)

8


2.2. Reduce the pressure within the hydrate zoneReduce the pressure within the hydrate zone

ti c

ktrφμ948

=

φ = 30%

μ= 1 cp

ct= 1×10–5 psi–1

K(SH) = 0.01 mD

0

50

100

150

200

250

300

0 0.5 1 1.5 2 2.5 3

Time (years)

r i (ft

)

9

Development of Analytical ModelDevelopment of Analytical Model

AssumptionsAssumptions

Deep decompositionDeep decompositionNo vertical gradient (timeNo vertical gradient (time--scale of one month)scale of one month)

TankTank--type model (zerotype model (zero--dimensional modeling)dimensional modeling)No radial gradient (timeNo radial gradient (time--scale of one month)scale of one month)

Equilibrium decompositionEquilibrium decomposition

Complete contact between the gas and the hydrateComplete contact between the gas and the hydrate

No water flowNo water flow

Constant gas production rateConstant gas production rate

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A Material (& Energy) Balance A Material (& Energy) Balance EquationEquation

Material BalanceMaterial Balance

GGpp = = q.tq.t

GGHH = Gas generated from the= Gas generated from thehydrateshydrates

GGpp –– GGHH = Net gas produced= Net gas produced

⎟⎟⎠⎞

⎜⎜⎝⎛ −−=

GGG

Zp

Zp Hp

i

i 1

Heat equation: Heat equation:

Heat from cap and base Heat from cap and base ++ sensible heat sensible heat ==

Heat available for decomposition (Heat available for decomposition (GGHH))

Equilibrium relationEquilibrium relation ⎟⎠⎞

⎜⎝⎛ += T

cap exp

The three unknowns, The three unknowns, p, T, p, T, andand GGHH are foundare found

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Solutions (CIPC 2006Solutions (CIPC 2006--018)018)

( )( ) ( )

⎥⎥⎦

⎤

⎢⎢⎣

⎡

⎟⎟⎠

⎞

⎜⎜⎝

⎛+

Δ+

−−

=

13

81 tCkcHH

cAHBG

TTZpZp

qtb

prrcrpH

pHf

oei

oeiioe

p

ρπρρ

ρ

⎟⎠⎞⎜

⎝⎛ += T

cap exp

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Solutions (SPE 102234)Solutions (SPE 102234)

HSTc

SteHH

p

Δ

Δ=

φρρ

2//HGq

N fpp α= 2/

/HTbNb α

Δ=

⎥⎦

⎤⎢⎣

⎡+−⎟⎟

⎠

⎞⎜⎜⎝

⎛−= S

rr

khTTpq

w

e

tsc

scwwf 4

3lnπ

ψψ

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Validation against Numerical Validation against Numerical Simulator (Simulator (HydrsimHydrsim))

Heat flowHeat flowConduction and convectionConduction and convectionDecomposition heat of hydrateDecomposition heat of hydrateHeat input from the cap/base rockHeat input from the cap/base rockHeat output by the producing fluidsHeat output by the producing fluids

Fluid flowFluid flowMultiMulti--phase flow through porous mediaphase flow through porous mediaGeneration of fluids due to decompositionGeneration of fluids due to decompositionGravity, capillary and viscous forcesGravity, capillary and viscous forces

Intrinsic Kinetics of decompositionIntrinsic Kinetics of decompositionThe KimThe Kim--Bishnoi modelBishnoi model

No No geomechanicalgeomechanical changeschanges

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Base CaseBase Case

OGIP - Hydrate= 680 MMSCF

OGIP - Free Gas= 160 MMSCF

30 ft

10 ft

Heat

Heat Heat

q = 1 MMSCF/day

pi = 1240 psiaTi = 53 F

φ = 30%

K = 50 mD

Swi= 0.2

1490 ft

Heat

One well per 160 acresOne well per 160 acres

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Validation Validation –– Average PressureAverage PressureVarious CasesVarious Cases

PorosityPorosity

Thermal conductivityThermal conductivity

Production rateProduction rate

Net payNet pay

Drainage areaDrainage area

Initial PressureInitial Pressure

PermeabilityPermeability

300

400

500

600

700

800

900

1000

1100

1200

1300

0 12 24 36 48Time (months)

Aver

age

Pres

sure

(psi

a)

Ti=43 Fpi=650 psia

Base

H=60 fth= 20 ft

q=2 MMSCF

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Validation Validation –– Hydrate RecoveryHydrate Recovery

0%

5%

10%

15%

20%

25%

30%

35%

40%

45%

50%

0 12 24 36 48Time (months)

Hyd

rate

Rec

over

y (%

)

Ti=43 Fpi=650 psia

H=10 fth= 3 ft

H=60 fth= 20 ft

q=2 MMSCF

Somewhat optimistic!Somewhat optimistic!

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Validation Validation –– Flowing BHPFlowing BHP

300

400

500

600

700

800

900

1000

1100

1200

1300

0 12 24 36 48Time (months)

Bot

tom

hole

Pre

ssur

e (p

sia)

Ti=43 Fpi=650 psia

Base

H=60 fth= 20 ft

q=2 MMSCF

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Prospect EvaluationProspect EvaluationUncertain Input ParametersUncertain Input Parameters

Thickness of the hydrate layer (10, 30, 50 ft)Thickness of the hydrate layer (10, 30, 50 ft)

Thickness of the free gas zone (3, 10, 30 ft)Thickness of the free gas zone (3, 10, 30 ft)

Hydrate Saturation (0.5, 0.6, 0.8)Hydrate Saturation (0.5, 0.6, 0.8)

PorosityPorosity

Drainage AreaDrainage Area

Equilibrium relationEquilibrium relation

Triang(0.2, 0.3, 0.5)

0

1

2

3

4

5

6

7

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

0.55

5.0% 5.0%90.0%0.2387 0.4452

Triang(10, 30, 50)

Val

ues

x 10

^-2

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

5 10 15 20 25 30 35 40 45 50 55

5.0% 5.0%90.0%16.32 43.68

Triang(3, 10, 30)

Val

ues

x 10

^-2

0

1

2

3

4

5

6

7

8

0 5 10 15 20 25 30 35

5.0%90.0%6.07 24.80

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0 2 4 6 8 10 12 14 16Total and Free Gas In Place (BCF)

Total vs. Free Gas In PlaceTotal vs. Free Gas In Place

-0.5 0 0.5 1

HH

hf

Sw

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Hydrate RecoveryHydrate Recovery

0% 10% 20% 30% 40% 50% 60%Hydrate Recovery at 5 years

-1 -0.5 0 0.5

HH

SW

hf

⎥⎦

⎤⎢⎣

⎡+= cbh NSteNR τ

πτ

38

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Bottomhole PressureBottomhole Pressure

300 400 500 600 700 800 900 1000Bottomhole Pressure at 5 years

Freezing at 330 Freezing at 330 psiapsia

⎥⎦

⎤⎢⎣

⎡+−⎟⎟

⎠

⎞⎜⎜⎝

⎛−= S

rr

khTTpq

w

e

tsc

scwpwf 4

3lnπ

ψψ

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Hydrate Contribution in RateHydrate Contribution in Rate

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.5 1 1.5 2 2.5 3Time (years)

Gen

erat

ion

Rat

e (M

MSC

F/da

y)

P90 (OGIP)P90 (OGIP)



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Why Analytical?Why Analytical?

Limited data requires risk analysis (hundredLimited data requires risk analysis (hundred’’s of runs)s of runs)

SpeedSpeed--up factorup factor

One simulation run: One simulation run: 10 hours10 hours

10,000 analytical runs:10,000 analytical runs: 2 minutes2 minutes

SpeedSpeed--up factor:up factor: 33××101066

Availability and ease of useAvailability and ease of use

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Reserve EstimationReserve Estimation

pwf Analytical OGIP

Compare the OGIPs

OGIP Simulator

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ConclusionsConclusions

For the cases studiedFor the cases studiedHydrate contribution to gas production was significantHydrate contribution to gas production was significant

A A ““simplesimple”” material (and energy) balance equation was material (and energy) balance equation was developeddeveloped

The simple model allows prospect evaluation and large number The simple model allows prospect evaluation and large number of runs required in risk analysisof runs required in risk analysis

Evaluate the upside due to contribution of hydratesEvaluate the upside due to contribution of hydrates

Etc.Etc.

In an inverse mode, the model can be used for reserve In an inverse mode, the model can be used for reserve estimationestimation

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AcknowledgmentsAcknowledgments

H. Hong, S. Gerami, A. H. Hong, S. Gerami, A. ShahbaziShahbazi, , ……

University of Calgary, Hydrate Resource Recovery ConsortiumUniversity of Calgary, Hydrate Resource Recovery Consortium

FeketeFekete Associates Inc and Mineral Management ServicesAssociates Inc and Mineral Management Services

Imperial Oil, CMG, GSC, NSERC, AERI, Imperial Oil, CMG, GSC, NSERC, AERI, NRCanNRCan

MallikMallik Research team, Drs. Scott Research team, Drs. Scott DallimoreDallimore & Fred Wright& Fred Wright

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Questions?Questions?

Thank you!Thank you!

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