Post on 28-Dec-2015
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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
Properties of the Rock Material
Permeability – Persamaan Darcy’s
6
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
Properties of the Rock Material
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
10
Static Rock-Fluid Properties
Wettability
Sudut kontak < 90° (water-wet)
Sudut kontak > 90° (oil-wet)
Sudut kontak = 90° (neutral)
11
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
Static Rock-Fluid Properties
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
Static Rock-Fluid Properties
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
Static Rock-Fluid Properties
Wettability
14
Capillary pressure - perbedaan tekanan antar muka dua fluida tidak membasahi pada sistem kapiler (porous)
Static Rock-Fluid Properties
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
Static Rock-Fluid Properties
Capillary Pressure
16
Capillary Pressure Curve menyatakan distribution air di dalam reservoir
Terdapat interval saturation yang secara gradual berubah dari 100% hingga saturasi air konate < 20%
Static Rock-Fluid Properties
Capillary Pressure
17
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
Static Rock-Fluid Properties
Capillary Pressure
18
OWC
Dep
th
Water Saturation, Swc
Top of OW
Transition Zone
5000
5800
0 100%
Sw = Swir
OWC
Dep
th
Water Saturation, Swc
Top of OW
Transition Zone
5000
5800
0 100%
Sw = Swir
OWC
Dep
th
Water Saturation, Swc
Top of OW
Transition Zone
5000
5800
0 100%
Sw = Swir
OWC
Dep
th
Water Saturation, Swc
Top of OW
Transition Zone
5000
5800
0 100%
Sw = Swir
Static Rock-Fluid Properties
Capillary Pressure
19
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
20
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
21
abs
effr
k
kk
Dynamic Rock-Fluid Properties
Relative Permeability
22
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
Dynamic Rock-Fluid Properties
Pengaruh Wettability pada Relative Permeability
23
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”
Dynamic Rock-Fluid Properties
Pengaruh Wettability pada Relative Permeability
25
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 ?
Dynamic Rock-Fluid Properties
Pengaruh Wettability pada Relative Permeability
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.
Dynamic Rock-Fluid Properties
Pengaruh Wettability pada Relative Permeability
27
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
Dynamic Rock-Fluid Properties
Mobility
28
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.
Dynamic Rock-Fluid Properties
Distribusi Saturasi Selama Pendesakan Fluida Tak Tercampur
29
Penampang bagian water drive reservoir dengan distrbusi saturasi uniform.
Hubungan saturasi terhadap jarak distance diperlihatkan pada gambar bawah.
Dynamic Rock-Fluid Properties
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 :
Dynamic Rock-Fluid Properties
Distribusi Saturasi Selama Pendesakan
Fluida Tak Tercampur
31
Fluid Displacement Characteristics
with Initial Distribution (After Slider)
Fraksi fluida pendesak dibelakang front akan meningkat terhadap jarak
Dynamic Rock-Fluid Properties
Perhitungan Saturasi Selama Pendesakan
32
Example oil-water relative permeabilities
Dynamic Rock-Fluid Properties
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
33
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:
Dynamic Rock-Fluid Properties
Penentuan Kurva Fractional Flow
34
ow
ww
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:
Penentuan Kurva Fractional Flow
35
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
Penentuan Kurva Fractional Flow
36
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
37
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
Penentuan Kurva Fractional Flow
38
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?)
Penentuan Kurva Fractional Flow
39
Key points about fractional flow curves
Dynamic Rock-Fluid Properties
Penentuan Kurva Fractional Flow
40
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
Key points about fractional flow curves
Dynamic Rock-Fluid Properties
Penentuan Kurva Fractional Flow
41
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
Key points about fractional flow curves
Dynamic Rock-Fluid Properties
Penentuan Kurva Fractional Flow
42
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?
Dynamic Rock-Fluid Properties
Penentuan Kurva Fractional Flow
43
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