Sifat Fisika Batuan Dan Fluida

1

SIFAT FISIKA

BATUAN dan FLUIDA

Sifat fisik Batuan: Porosity

Pore size distribution

Permeability

Formation compressibility

Sifat statis batuan-fluida (interaksi batuan & fluids di dalam pori):

Wettability & contact angle

Capillary pressure & interfacial tension

Irreducible & connate water saturation

Residual oil saturation

Sifat Dinamis batuan-fluida (interaksi batuan & fluida):

Relative permeability

Mobility

Saturation distribution during immiscible fluid displacement

Sifat Fisik Batuan Reservoir

2

Original or primary porosity - dibentuk bersamaan dgn pengendapan batuan, terkompaksi dan tersemen bersama menjadi matriks

Induced or secondary porosity - berkembang akibat proses geologi yang terjadi setelah pengendapan

Total porosity - total rongga batuan dibagi bulk volume batuan

Effective porosity - ratio rongga yang saling berhubungan terhadap bulk volume batuan

Properties of the Rock Material Porosity

3

Properties of the Rock Material

Porosity

4

VolumeBulk

VolumeVoidPorosity

VolumeBulk

VolumePorectedInterconnePorosityEffective e

VolumeBulk

VolumePoreTotalPorosityTotal T

grainscementedbeweenvolumeVoid

grainssolidbyoccupiedVolumeRockVolumeBulk

Properties of the Rock Material Porosity

Sandstones = 1% - 38%

rata-rata = 20%

Limestone & dolomite rata-rata = 10%

5

Pore Space in Packing of Uniform Spheres

Persamaan Darcy’s untuk aliran horizontal linear melalui media pori


Permeability – Persamaan Darcy’s

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A

Q

Q

Dp

p1

p2

L

L

pp

μ

Akq

1 2

21 ppA

Lμqk

dimana: q = volumetric rate (cm3/sec)

k = permeability (darcies)

A = area (cm2)

m = viscosity (cp)

p1 = upstream pressure (atm)

p2 = downstream pressure (atm)

L = length of porous media (cm)

Batuan memiliki permeabilitas satu Darcy akan mengalirkan fluida berviskositas satu centipoise melalui luasan satu cm2 dengan laju alir satu centimeter cubic per detik pada gradient tekanan sebesar satu atmosphere per cm. Biasanya 1 Darcy terlalu besar untuk ukuran batuan reservoir, sehingga millidarcy, merupakan satuan

yang biasa digunakan

1000 md = 1 D

Properties of the Rock Material Permeability – Persamaan Darcy’s

7

Persamaa Darcy’s untuk aliran horisontal / linier :

q = volumetric flow rate of liquid (bbl/day)

k = permeability (md)

A = flow area (ft2)

p1 = upstream pressure (psi)

p2 = downstream pressure (psi)

m = fluid viscosity (cp)

L = thickness of porous media (ft)

Properties of the Rock MaterialPermeability – Persamaan Darcy’s

8

Lμ

ppAk1.1271x10q

213

Asumsi persamaan Darcy’s adalah: Aliran Incompressible flow

Viskositas konstan

Aliran laminar sangat pelan

Aliran Steady state


Permeability – Persamaan Darcy’s

9

Ketika menggunakan persamaan Darcy’s, apakah batasab tersebut sepenuhnya dapat terpenuhi untuk mendapatkan permeability menjadi akurat ?

Permeabilitas

Sifat batuan & bukan fluida yang mengair melaluinya, menyebabkan fluida 100% mensaturasi seluruh pori batuan

Permeabilitas Absolute

Permeabilitas batuan yang di saturasi satu jenis fluida

Permeabilitas Effective

Permeabilitas batuan bila pada batuan tersebut disaturasi oleh lebih dari satu fluida

Jumlah dari permeabilitas effective utk fluida yang berlainan selalu < permeabilitas absolute-nya

Properties of the Rock Material Permeabilitas Absolute dan Effective

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Static Rock-Fluid Properties

Wettability

Sudut kontak < 90° (water-wet)

Sudut kontak > 90° (oil-wet)

Sudut kontak = 90° (neutral)

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Forces in Equilibrium at Oil-

water Interface

Wettability - kecenderungan satu fluida ter-adesi di

permukaan padatan dibandingkan fluida taktercampur

lainnya

Pada umumnya reservoirs, merupakan:

25% water-wet

25% oil-wet

50% intermediate or mixed wettability

Efficiency Pendesakan fluida nonwetting mendesak fluida membasahi biasanya lebih kecil dibandingkan fluida wetting terhadap non-wetting


Wettability

12

Oil Wet Water Wet

Sand Grain

Water

Oil

Sand Grain

Water

Oil

Drainage - apabila fasa non-wetting displaces fasa wetting

Imbibition – apabila fasa wetting displaces fasa non-wetting


Wettability

13

Wettability dapat diidentifikasi dengan cara:

Apabila air produksi memiliki komposisi sama dengan air conat, reservoir bersifat water-wet.

Apabila air produksi sama dengan air injeksi, ada dua kemungkinan:

Reservoir adalah oil-wet.

Air injeksi melewati zona porous yang sangat tipis atau fracture, dan karenanya tidak mempunyai kesempatan kontak secara cukup dengan connat water kecuali pada sistem dengan proses water breakthrough yang lama


Wettability

14

Capillary pressure - perbedaan tekanan antar muka dua fluida tidak membasahi pada sistem kapiler (porous)


Capillary Pressure

15

Hubungan antara saturasi air, Sw, pada setiap titik di media pori dengan tekanan kapiler-nya didefinisikan sebagai capillary-pressure curve

Dua tipe:

Drainage curves - memperlihatkan perubahan saturasi fasa non-wetting mendesak fasa wetting

Imbibition curves - memperlihatkan perubahan saturasi fasa wetting mendesak fasa non-wetting


Capillary Pressure

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Capillary Pressure Curve menyatakan distribution air di dalam reservoir

Terdapat interval saturation yang secara gradual berubah dari 100% hingga saturasi air konate < 20%


Capillary Pressure

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Example of a typical capillary pressure curve and the corresponding

vertical fluid distribution in the reservoir

Layer yang kurang permeabel memiliki zona transisi yang lebih lebar dan Saturasi air konat lebih besar

Kesalahan dalam menentukan Tekanan Kapiler dapat menyebabkan estimasi OOIP yang optimistik

Capillary pressure curves menyatakan sifat sample & kehati-hatian diperlukan ketika scaling up ke skala reservoir

Untuk menjamin distribusi saturasi dari data pengukuran tekanan kapiler, saturasi harus dikalibrasi terhadap logs


Capillary Pressure

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OWC

Dep

th

Water Saturation, Swc

Top of OW

Transition Zone

5000

5800

0 100%

Sw = Swir

OWC

Dep

th


Top of OW

Transition Zone

5000

5800

0 100%

Sw = Swir

OWC

Dep

th


Top of OW

Transition Zone

5000

5800

0 100%

Sw = Swir

OWC

Dep

th


Top of OW

Transition Zone

5000

5800

0 100%

Sw = Swir


Capillary Pressure

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Irreducible water saturation, Swir

Minimum saturation pada capillary pressure curve vertical

Maximum saturation tanpa aliran air

Connate water saturation, Swc

Saturasi air asli dalam reservoir – yang dapat lebih besar atau sama dengan Swir

Jika Swc > Swir berarti fasa mobile

Pada beberapa perhitungan reservoir, irreducible & connate water saturations dapat diasumsikan identik

Dipengaruhi oleh wettability batuan - cenderung lebih rendah pada batuan oil-wet dibandingkan pada water-wet rocks

Irreducible & Connate Water Saturation

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Relative permeability - perbandingan permeabilitas effective terhadap

permeabilitas absolute-nya

Persamaan Darcy's, aslinya diformulasikan untuk digunakan pada media pori yang disaturasi hanya dengan satu fluida . . yaitu air

Dynamic Rock-Fluid Properties

Relative Permeability

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abs

effr

k

kk


Relative Permeability

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ds

dz g ρ -

ds

dp

μ

A k - = q o

o

o

o

o

ds

dz g ρ -

ds

dp

μ

A k - = q g

g

g

g

g

ds

dz g ρ -

ds

dp

μ

A k - = q w

w

w

w

w

k

k = k

oro

k

k = k

grg

k

k = k

wrw


Pengaruh Wettability pada Relative Permeability

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Examples of relative permeability curves

Kharakteristik water-oil relative permeability untuk water-wet & oil-wet reservoirs:

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1.0

0.8

0.6

0.4

0.2

0 0 20 40 60 80 100

Water

Oil

Water Sat., % PV

Re

lati

ve

Pe

rme

ab

ilit

y F

racti

on

Typical water/oil relative permeability

characteristics - strongly water-wet rock

Rela

tiv

e P

erm

eab

ilit

y F

racti

on

1.0

0.8

0.6

0.4

0.2

0 0 20 40 60

Water Sat., % PV

80 100

Water

Oil

Typical water/oil relative permeability

characteristics - strongly oil-wet rock

Re

lati

ve

Pe

rme

ab

ilit

y F

racti

on

Craig “rules of thumb”



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Water-Wet Oil-Wet

Connate water saturation Usually greater than 20-25%PV

Generally less than15%PVFrequently less than10%PV

Saturation at which oil andwater relative permeabilitiesare equal

Greater than 50%water saturation

Less than 50% watersaturation

Relative permeability to waterat maximum water saturation(i.e., floodout)

Generally less than30%

Greater than 50% andapproaches 100%

Ini adalah oil-water relative permeability plot untuk "T" Sand di lapangan KB

Menggunakan Craig rules of thumb, apa jenis batuan reservoir “T” sand ?



26

core sample dari lab:

Calculate krw, krog, krow, and kro for the values of Sw listed in the table in your manual. This is an oil-water system.



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Swir Irreducible water saturation 0.20

Sorw Residual oil saturation to water 0.48

Swc Connate (initial) water saturation 0.20

Sgc Critical gas saturation 0.00

Sorg Residual oil saturation to gas 0.54

ew Exponent for krw equation 1.6

eow Exponent for krow equation 2.0

eg Exponent for krg equation 2.0

eog Exponent for krog equation 3.0

krwro Water relative permeability at residual oil (to water) 0.02

krocw Oil relative permeability at connate water saturation 0.73

krgro Gas relative permeability at residual oil (to gas at connate watersaturation)

0.3

Pada persamaan Darcy’s, mobility sebagai berbanding lurus dengan kecepatan alir fluida dan berbanding terbalik terhadap gradien tekanan

Jadi water mobility is:

dan oil mobility is:

Mobility - ukuran seberapa mudah satu fluida melalui reservoir pada kondisi batuan dan fluida tertentu


Mobility

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w

w

μ

k

o

o

μ

k

Miscible displacement - apabila dua fluida dapat bercampur secara proporsional dan tak terpisahkan menjadi dua fasa

Minyak dan Air tidak dapat bercampur, sehingga merupakan fluida tak tercampur.

Immiscible displacement – apabila air mendesak minyak seperti pada water drive atau project injeksi air.

Secara Umum, karena air mendesak minyak, maka akan terjadi distribusi saturasi yang seragam pada suatu daerah diskontinuitas saturasi didepannya setelah pemindahan oleh air.


Distribusi Saturasi Selama Pendesakan Fluida Tak Tercampur

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Penampang bagian water drive reservoir dengan distrbusi saturasi uniform.

Hubungan saturasi terhadap jarak distance diperlihatkan pada gambar bawah.


Distribusi Saturasi Selama Pendesakan Fluida Tak

Tercampur

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Schematic of Saturation Profile (After Slider)

Slider, H. C., “Practical Petroleum Reservoir Engineering

Methods”, Petroleum Publishing Corp.

Minyak bergerak kearah sumur produksi dan air masuk dari aquifer atau sumur injeksi, distibusi saturasi akan berubah terhadap :


Distribusi Saturasi Selama Pendesakan

Fluida Tak Tercampur

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Fluid Displacement Characteristics

with Initial Distribution (After Slider)

Fraksi fluida pendesak dibelakang front akan meningkat terhadap jarak


Perhitungan Saturasi Selama Pendesakan

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Example oil-water relative permeabilities


Penentuan Kurva Fractional Flow

Fraksi air fw disebut water cut

Dasar fractional flow :

Metode Analitis didasarkan pada material balance dari 2 fasa fluida incompressible

Assumsi system reservoir homogeneous

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Example of Fraction Flow Curve (After Slider)

Fractional flow untuk air mendesak minyak:

Sesuai persamaan, asumsi aliran horizontal & tekanan kapiler diabaikan :

If gravity effects (densities of the fluids) & non-horizontal flow (dip of the reservoir) are significant:



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ow

ww

qq

qf

o

w

rw

ro

wNO

μ

μ

k

k1

1f

o

w

rw

ro

to

ro

w

μ

μ

k

k1

qμ

sinaΔγKA0.000488k1

f

A water drive reservoir is of such size & shape that water encroachment to first line of producers can be treated as linear flow. The water drive is sufficiently active that fluid flow is steady state. The withdrawal rate from the reservoir averages 2,830 reservoir BPD. Reservoir data are as follows:


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Item Symbol Value

Average formation dip, 15.5

Average “width” of reservoir, feet 8000

Reservoir thickness, feet 30

Average cross-sectional area, feet2

A 240,000

Permeability, mD K 108

Connate water (irreducible water) saturation, % Swc 16

Reservoir oil specific gravity o 1.01

Reservoir oil viscosity, cps mo 1.51

Reservoir water specific gravity w 1.05

Reservoir water viscosity, cps mw 0.83

Calculate the fractional flow for this reservoir corresponding to the saturations listed above for: Inclusion of dip and gravity effects Excluding dip and gravity effects Use oil viscosity of 8.6 cps & exclude dip/gravity effects


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Relative Permeability Data:

Sw, % krw kro

79 (1 – Sorw) 0.63 0.0075 0.54 0.0265 0.37 0.0955 0.23 0.2345 0.13 0.4435 0.06 0.7325 0.02 0.9416 (Swc) 0.00 0.98

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Welge Method

1. Estimate OOIP

2. Plot relative permeability curves

3. Estimate average reservoir dip

4. Calculate & plot fractional flow curve, fw

5. Determine water saturation at breakthrough, Swbt, from fractional flow curve

6. Determine average Sw behind the flood front at time of breakthrough

7. Calculate the slope of the fractional flow curve for each water saturation on the relative permeability table

8. Calculate the pore volumes of cumulative injected water required to obtain each water saturation

9. Calculate the cumulative water injection (BBLS) required to obtain each water saturation

10. Calculate the time needed to obtain each water saturation

11. Calculate oil & water production rates for each water saturation

12. Plot oil & water rate versus time

13. Calculate mobility ratio (favorable or adverse?) Ch 2 - 37

1. Estimate OOIP

2. Plot relative permeability curves

3. Estimate average reservoir dip

4. Calculate and plot fractional flow curve, fw

5. Determine water saturation at breakthrough, Swbt., from fractional flow curve

6. Determine average Sw behind the flood front at time of breakthrough

7. Calculate the slope of the fractional flow curve for each water saturation on the relative permeability table


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8. Calculate the pore volumes of cumulative injected water required to obtain each water saturation

9. Calculate the cumulative water injection (BBLS) required to obtain each water saturation

10. Calculate the time needed to obtain each water saturation

11. Calculate oil and water production rates for each water saturation

12. Plot oil and water rate versus time

13. Calculate mobility ratio (favorable or adverse?)


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Key points about fractional flow curves



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qw qo, qw

sw

x

Same Sbt for all fronts

Average saturation behind the flood front is

always greater than Sw at the front

Saturation ahead of the flood front is Swc Sharp front




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Fractional Flow Curves

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.2 0.4 0.6 0.8 1 Water Saturation, Sw

Fra

cti

on

al F

low

, f w

mo/mw= 0.5

mo/mw= 10

mo/mw= 2

0.5 2.0 10.0

Sw at breakthrough

Sw behind the front

Sw should be as

close to 1 as

possible for best

sweep efficiency




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At breakthrough: (tangent)fofslopeMaximumS

fw

w

w

bt

Behind the flood front:

12

12

bt

ww

wwww

w

w

SS

ffSS

S

f

At the flood front:: 0.0SSS

fbtww

w

w

Which of these fluid displacement plots illustrates the best waterflood candidate?



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Saturation Profile (Flood Front)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

X

Sw

0.5μ

μ

w

o

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

X

Sw

2.0μ

μ

w

o

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

X

Sw

10.0μ

μ

w

o

Sifat Fisika Batuan Dan Fluida

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