Kuliah 6-Perembesan Air
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Transcript of Kuliah 6-Perembesan Air
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Kuliah 6Perembesan Air (Water-Influx)
Oleh: Taufan Marhaendrajana, PhD
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Definisi
Water influx (perembesan air) adalah aliran air ke reservoir dari aquifer yang bersinggungan karena penurunan tekanan di reservoir akibat produksi.
Besarnya rembesan air ini dipengaruhi oleh:
Dimensi dari aquifer
Permeabilitas aquifer
Luas kontak aquifer dengan reservoir
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Klasifikasi Aquifer
Many gas and oil reservoirs produced by a mechanism termed water drive. Often this is called natural water drive to distinguish it from artificial water drive that involves the injection of water into the formation. Hydrocarbon production from the reservoir and the subsequent pressure drop prompt a response from the aquifer to offset the pressure decline. This response comes in a form of water influx, commonly called water encroachment, which is attributed to:
Expansion of the water in the aquifer
Compressibility of the aquifer rock
Artesian flow where the water-bearing formation outcrop is located
structurally higher than the pay zone
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Interaksi Reservoir-Aquifer
Reservoir-aquifer systems are commonly classified on the basis of:
Degree of pressure maintenance
Flow regimes
Outer boundary conditions
Flow geometries
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Degree of Pressure MaintenanceBased on the degree of the reservoir pressure maintenance provided by the aquifer, the natural water drive is often qualitatively described as: Active water drive Partial water drive Limited water drive
The term active water drive refers to the water encroachment mechanismin which the rate of water influx equals the reservoir total productionrate.
Active water-drive reservoirs are typically characterized by a gradual and slow reservoir pressure decline. If, during any long period, the production rate and reservoir pressure remain reasonably constant, the reservoir voidage rate must be equal to the water influx rate.
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ew = Qo Bo + Qg Bg + Qw Bw
Water influx rate = oil flow rate + free gas flow rate + water production rate
where ew = water influx rate, bbl/dayQo = oil flow rate, STB/dayBo = oil formation volume factor, bbl/STBQg = free gas flow rate, scf/dayBg = gas formation volume factor, bbl/scfQw = water flow rate, STB/dayBw = water formation volume factor, bbl/STB
Contoh:Calculate the water influx rate ew in a reservoir whose pressure is stabilized at 3000 psi.
Given: initial reservoir pressure = 3500 psi; Qo = 32,000 STB/day; Bo = 1.4 bbl/STB; GOR = 900 scf/STB; Rs = 700 scf/STB; Bg = 0.00082 bbl/scf; qw = 0; Bw = 1.0 bbl/STB
Jawaban:ew = (1.4) (32,000) + (900 700) (32,000) (0.00082) + 0 = 50,048 bbl/day
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Outer Boundary Conditions
The aquifer can be classified as infinite or finite (bounded). Geologically all formations are finite, but may act as infinite if the changes in the pressure at the oil-water contact are not felt at the aquifer boundary. Some aquifers outcrop and are infinite acting because of surface replenishment. In general, the outer boundary governs the behavior of theaquifer and, therefore:
a. Infinite system indicates that the effect of the pressure changes at the oil/aquifer boundary can never be felt at the outer boundary. This boundary is for all intents and purposes at a constant pressure equal to initial reservoir pressure.
b. Finite system indicates that the aquifer outer limit is affected by the influx into the oil zone and that the pressure at this outer limit changes with time.
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Flow Regimes
There are basically three flow regimes that influence the rate of water influxinto the reservoir. As previously described in Chapter 6, those flow regimes are:
a. Steady-stateb. Semisteady (pseudosteady)-statec. Unsteady-state
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Flow GeometriesReservoir-aquifer systems can be classified on the basis of flow geometry as:
a. Edge-water driveb. Bottom-water drivec. Linear-water drive
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RECOGNITION OF NATURAL WATER INFLUX
A comparatively low, and decreasing, rate of reservoir pressure decline with increasing cumulative withdrawals is indicative of fluid influx.
If the reservoir pressure is below the oil saturationpressure, a low rate of increase in produced gas-oil ratio is also indicative of fluid influx.
Early water production from edge wells is indicative of water encroachment.
Calculation of increasing original oil-in-place from successive reservoir pressure surveys by using the material balance assuming no water influx is also indicative of fluid influx.
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oNEF
wpgspop BWBRRBNF
gssioioo BRRBBE )()(
NF
EoO
Indication of water influx
No water influx
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WATER INFLUX MODELS
The mathematical water influx models that are commonly used in the petroleum industry include: Pot aquifer Schilthuis steady-state The Van Everdingen-Hurst unsteady-state
Edge-water drive Bottom-water drive
The Carter-Tracy unsteady-state Fetkovichs method
Radial aquifer Linear aquifer
Fast Convolution Method (FCM)
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Water Influx CalculationUsing POT Aquifer Model
Water influx = (aquifer compressibility) (initial volume of water)(pressure drop)
We = (cw + cf) Wi (pi p)
Mempertimbangkan area of contact:
We = (cw + cf) Wi f (pi p)
where We = cumulative water influx, bblcw = aquifer water compressibility, psi1cf = aquifer rock compressibility, psi1Wi = initial volume of water in the aquifer, bblpi = initial reservoir pressure, psip = current reservoir pressure (pressure at oil-water contact), psif = encroachment angle
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where ra = radius of the aquifer, ftre = radius of the reservoir, fth = thickness of the aquifer, ft = porosity of the aquifer
615.5
22 hrrW eai
360
f
Radial aquifer geometry
Contoh:Calculate the cumulative water influx that results from a pressure drop of 200 psi at the oil-water contact with an encroachment angle of 80. The reservoir-aquifer system is characterized by the following properties:
Reservoir Aquifer
Radius, ft 2600 10,000
porosity 0.18 0.12
cf, psi-1 4x10-6 3x10-6
cw, psi-1 5x10-6 4x10-6
h, ft 20 25
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SolutionStep 1. Calculate the initial volume of water in the aquifer.
Step 2. Determine the cumulative water influx.
MMbblWi 5.156
615.5
12.025600,2000,10 22
We = (4 + 3) 10-6 (156.5 10-6 ) (80/360) (200) = 48,689 bbl
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Water Influx CalculationUsing Schilthuis Steady-State Model
where ew = rate of water influx, bbl/dayk = permeability of the aquifer, mdh = thickness of the aquifer, ftra = radius of the aquifer, ftre = radius of the reservoirt = time, daysC = water influx constant, bbl/psi/day
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Contoh:The data given :pi = 3500 psi; p = 3000 psi; Qo = 32,000 STB/day; Bo = 1.4 bbl/STB; GOR = 900 scf/STB; Rs = 700 scf/STB; Bg = 0.00082 bbl/scf; Qw =0; Bw = 1.0 bbl/STBCalculate Schilthuis water influx constant.SolutionStep 1. Solve for the rate of water influx ew.
ew = (1.4) (32,000) + (900 700) (32,000) (0.00082)+ 0= 50,048 bbl/day
Step 2. Solve for the water influx constant
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Cumulative Water Influx:
where We = cumulative water influx, bblC = water influx constant, bbl/day/psit = time, dayspi = initial reservoir pressure, psip = pressure at the oil-water contact at time t, psi
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Contoh: (class exercise)The pressure history of a water-drive oil reservoir is given below:
t, days p, psi
0 3500
100 3450
200 3410
300 3380
400 3340
The aquifer is under a steady-state flowing condition with an estimated water influx constant of 130 bbl/day/psi. Calculate the cumulative water influx after 100, 200, 300, and 400 days using the steady-state model.
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Water Influx CalculationUsing Van Everdingen-Hurst Unsteady-State Model
The model solution can be used to determine the water influx in the following systems:
Edge-water-drive system (radial system) Bottom-water-drive system Linear-water-drive system
hfrcB
pWBW
et
eDe
2119.1
where :We = cumulative water influx, bblB = water influx constant, bbl/psip = pressure drop at the boundary, psiWeD = dimensionless water influxf = ratio of encroachment angle
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Dimensionless Water Influx
Edge Water Drive
Idealized Radial Flow Model
2
310328.6et
Drc
ktt
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Contoh:Calculate water influx at the end of 1, 2, and 5 years into a circular reservoir with an aquifer of infinite extent. The initial and current reservoir pressures are 2500 and 2490psi, respectively. The reservoir-aquifer system has the following properties.
Reservoir Aquifer
Radius, ft 2000 infinite
porosity 0.15 0.20
cf, psi-1 2x10-6 0.3x10-6
cw, psi-1 1x10-6 0.7x10-6
h, ft 20 25
k, md 50 100
w, cp 0.5 0.8
SolutionStep 1. Calculate the total compressibility coefficient ct.ct = 0.7 (106) + 0.3 (103) = 1 106 psi1
Step 2. Determine the water influx constant.B = 1.119 (0.2) ( 1 106) (2000)2 (25) (360/360) = 22.4
Step 3. Calculate the corresponding dimensionless time after 1, 2, and 5 years.
)2000)(101)(8.0)(2.0(
10010328.6
26
3
ttD
t (tahun) t (hari) tD
1 365 361
2 730 722
5 1825 1805
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Step 4. Using Table 10-1, determine the dimensionless water influx WeD
t (tahun) t (hari) tD WeD
1 365 361 123.5
2 730 722 221.8
5 1825 1805 484.6
Step 5. Calculate the cumulative water influx.
eDe WW )24902500)(4.22(
t (tahun) t (hari) tD WeD We (bbl)
1 365 361 123.5 27664
2 730 722 221.8 49683
5 1825 1805 484.6 108550
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Change in Boundary Pressure
Boundary Pressure Versus Time
Illustration of superposition concept
eDe pWBW
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Contoh:Using the data given in previous Examples:
calculate the cumulative water influx at the end of 6, 12, 18, and 24 months. The predicted boundary pressure at the end of each specified time period is given below:
Reservoir Aquifer
Radius, ft 2000 infinite
porosity 0.15 0.20
cf, psi-1 2x10-6 0.3x10-6
cw, psi-1 1x10-6 0.7x10-6
h, ft 20 25
k, md 50 100
w, cp 0.5 0.8
t, months p, psi
0 2500
6 2490
12 2472
18 2444
24 2408
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Solution:
t, months t, days p, psi tD
0 0 2500 0
6 182.5 2490 90.2
12 365 2472 180.4
18 547.5 2444 270.7
B = 1.119 (0.2) ( 1 106) (2000)2 (25) (360/360) = 22.4
)2000)(101)(8.0)(2.0(
10010328.6
26
3
ttD
t = 6 months
tD = 180.4, WeD = 69.46We = (22.4) (2500-2490) (69.46) = 15559.04 bbl
t = 12 months
t, months
t, days p, psi Dp Dt DtD WeD We
0 0 2500 0 0
6 182.5 2490 10 12 360.9 123.5 24700
12 365 2472 18 6 180.4 69.46 28006.3
Total Water Influx 52706.3
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t = 18 months
t, months
t, days p, psi Dp, psi Dt, days DtD WeD We, bbl
0 0 2500 0 0
6 182.5 2490 10 547.5 541.3 173.7 38908.8
12 365 2472 18 365 360.9 123.5 49795.2
18 547.5 2444 28 182.5 180.4 69.46 43565.3
Total Water Influx, bbl 132269.3
t = 24 months ?
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Water Influx CalculationUsing Fetkovich Method
Equation of Water Influx
1 nanae ppUW
Where:
RB/psi615.5/)360/( 22 rat rrhcU
Radial Aquifer Linear Aquifer
RB/psi615.5/tcALU
RB/D/psi
4/3/ln
)360/(1008.7 3
ra rr
khJ
Aquifer Pressure
tnsnstnana eppepp 11211
1year,/365 UJ
RB/D/psi003381.0
L
kAJ
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Example of Water Influx CalculationUsing Fetkovich Method
Example:
h = 100 ftk = 200 mD = 0.25ct = 7x10
-6 psi-1
rr = 9200 ftR = 5 = 140o
Time
(years)
Pressure at OWC
(psia)
0 2740
1 2500
2 2290
3 2109
4 1949
5 1818
6 1702
7 1608
8 1535
9 1480
10 1460
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Example of Water Influx CalculationUsing Fetkovich Method
RB/psi27.77348
)920046000)(107)(100)(25.0)(360/140(
615.5/)()360/(
226
22
rat rrhcU
For T = 1 year:
RB/D/psi116.5
4/35ln)55.0(
)360/140)(100)(200(1008.7
4/3/ln
)360/(1008.7 33
ra rr
khJ
1year5498.0)27.77348/()5.116(365
psia2689
)1)(25002740()2740(
1
)1(5498.0
21)1(5498.0
)0()1(
21)0()1(
ee
eppepp tsst
aa
MMRB945.3)26892740(27.77348)1()0()1( aae ppUW
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Example of Water Influx CalculationUsing Fetkovich Method (Continued)
For T = 2 year:
psia2565
)1)(22902500()2689(
1
)1(5498.0
21)1(5498.0
)1()2(
21)1()2(
ee
eppepp tsst
aa
MMRB591.9)25652689(27.77348)2()1()2( aae ppUW