Enhance Gravity Inversion Result Using Integration of Time-lapse Surface and Borehole Microgravity

Enhance Gravity Inversion Result Using Integration of Time-lapse Surface and

Borehole MicrogravityBy:

Andika Perbawa(1)(2), Wawan G. A. K(3)

(1)Medco E&P Indonesia(2) Formerly Geophysical Engineering ITB

(3) Geophysical Engineering ITB

The Bali 2010 International Geosciences Conference and Exposition, Bali, Indonesia, 19-22 July 2010

Background Basic Theory Forward Modeling Inverse Modeling Analysis Conclusions Recommendations

Outline

Time-lapse microgravity survey Supporting production management, Monitoring fluid movement.

Acquisition At least two gravity measurements (Kadir, et. al., 2003).

Limitation in vertical resolution.

Time-lapse borehole microgravity survey Enhance the signal sensitivity, Sharpen vertical resolution.

Inversion Understanding distribution of density contrast.

Background


Outline

Basic Theory(equation)

(Plouff, 1976)

2

1

2

1

2

1,, )log()log(arctan

,,i j

iijkiiijkiijkk

iik

kijkrqpz yRyxRx

RZyxZGg

rqp

222kjiijk zyxR

kjiijk 111

Where:

∆ρ=(+)

Basic Theory (Gravity Anomaly)

∆gmgalmgal

1st measurement 2nd measurement

=

=

TLSM

TLBM

Density contrast

waterwater

oil oil

t1 t2 ∆t=t2-t1

µgal

µgal∆g

ρmatrix (gr/cc) ρoil (gr/cc) ρwater (gr/cc) Φ2.65 0.85 1 27%

Bulk Density Assumption (example)

ρb= (1- )Φ ρmatrix + Φ (So*ρoil+Sw*ρwater)

1st Condition (100% oil)ρb(1) = (100% - 27%)2.65 + 27%(100%*0.85 + 0%*1)ρb(1) = 2.16 gr/cc

2nd Condition (100% water)ρb(2) = (100% - 27%)2.65 + 27%(0%*0.85 + 100%*1)ρb(2) = 2.2 gr/cc

∆ρ=ρb(2)-ρb(1)

∆ρ=2.16-2.2

∆ρ=0.04 gr/cc

(Schön, 1995)

Time-lapse Borehole Microgravity Anomaly

ρ1=2

ρ1=2.1

ρ1=2.16

ρ1=2.3

ρ1=2.4

ρ2=2

ρ2=2.1

ρ2=2.2

ρ2=2.3

ρ2=2.4

∆ρ=0

∆ρ=0

∆ρ=0.04

∆ρ=0

∆ρ=0

- =

2ndcondition

1stcondition

Density contrast

TLBM response

(+)

(-)

ρ in (gr/cc)

Basic Theory(inversion)

Relationship between data and model parameter:

Damp least square inversion solution:

dGGGm

mGdTT 1

dGIGGm TT 12

(Grandis, 2008)

Damp Least Square Inversion

m : density contrast G : geometry factor matrixε : damping factorI : identity matrixd : gravity anomaly


Outline

Body Anomaly Geometry(Actual Density Contrast Distribution)

Δρ(gr/cc)

Borehole location

Positive anomaly (red)

Negative anomaly

(blue)

4 Layers

Layer-1Layer-2Layer-3Layer-4

(a) 3D view (b)map view

(c) Cross section

Forward Modeling(Time-lapse Surface Microgravity)

Body anomaly location (black rectangle)

ForwardModeling(Time-lapse Borehole Microgravity)

Separate into two bodies

∆ρ(-)∆ρ(+)


Outline

Actual Model TLSM Inversion

TLBM Inversion Joint Inversion

Δρ(gr/cc)

Actual model Δρ(gr/cc)

TLSM Inversion

Δρ(gr/cc)

TLBM Inversion Δρ(gr/cc)

Joint Inversion

Inversion Results

InversionComparison

(Layer-1)

Actual model Surface inversion

Borehole inversion Joint inversion

InversionComparison

(Layer-2)



InversionComparison

(Layer-3)



InversionComparison

(Layer-4)




Outline

Comparison of contrast density distribution (Northing-line Section)

Δρ(gr/cc)

Actual model

Joint inversion

Borehole inversion

Surface inversion

0 50 100 150 200 250 300 350

-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0.04

Density Profile at Layer 1

0 50 100 150 200 250 300 350

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0.04

Layer 2

0100

200300

-0.03

-0.02

-0.01

-3.46944695195361E-18

0.01

0.02

0.03

0.04

Layer 3

0 50 100 150 200 250 300 350

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0.04

Layer 4

Layer 4 Origin

Layer 4 from surface inversion

Layer 4 from All Borehole inversion

Layer 4 from Join Inversion

Initial model

TLSM

TLBM

Joint

(∆ρ) (∆ρ)

(∆ρ) (∆ρ)

Comparison of contrast density distribution(Easting-line Section)

Δρ(gr/cc)

Actual model

Joint inversion

Borehole inversion

Surface inversion

0 50 100 150 200 250 300 350 400

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0.04

Density Profile at Layer 1

0 50 100 150 200 250 300 350 400

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0.04

Layer 2

0100

200300

400

-0.03

-0.02

-0.01

-3.46944695195361E-18

0.01

0.02

0.03

0.04

Layer 3

0 100 200 300 400

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0.04

Layer 4

Layer 4 Originlayer 4 from surface inversionLayer 4 from all borehole inversionLayer 4 from join inversion

Initial model

TLSM

TLBM

Joint

(∆ρ) (∆ρ)

(∆ρ) (∆ρ)

RMS error (gr/cc)

surface inversion borehole inversion joint inversion

0.010 0.006 0.005

Error Analysis


Outline

Time-lapse Borehole Microgravity Forward modeling : good vertical resolution. Inverse modeling : increase sensitivity to detect

density contrast.

Joint inversion shows the best result to determine density contrast distribution.

Conclusions


Outline

Apply joint inversion for real data.

Try other inversion methods to optimize the result,

Try other models (more complex),

Analyze how much optimum boreholes that we need and the distance between them,

Recommendations

Thank You

Back Slide

Detail inversion result of TLSM

Inversion using 1 borehole

Δρ(gr/cc)

Inversion using 1 borehole

±75 meter radius

Error distribution of iteration

TLSM Inversion Error

TLBM Inversion Error

Joint Inversion Error

Resolution : 1-20 µgal Gas-oil ± 2 µgal Gas-water ± 5 µgal Oil-water 0.7-3 µgal Accessable casing up to 5½ inch. 14 degree from vertical.(Nabighian, et. al., 2005)

Instrument

Instrument ofboreholegravitymeter.(Goodell, R. R., 1964).

Enhance Gravity Inversion Result Using Integration of Time-lapse Surface and Borehole Microgravity

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