Kuliah 6Perembesan Air (Water-Influx)

Oleh: Taufan Marhaendrajana, PhD

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

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

Interaksi Reservoir-Aquifer

Reservoir-aquifer systems are commonly classified on the basis of:

Degree of pressure maintenance

Flow regimes

Outer boundary conditions

Flow geometries

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.

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

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.

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

Flow GeometriesReservoir-aquifer systems can be classified on the basis of flow geometry as:

a. Edge-water driveb. Bottom-water drivec. Linear-water drive

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.

oNEF

wpgspop BWBRRBNF

gssioioo BRRBBE )()(

NF

EoO

Indication of water influx

No water influx

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)

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

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

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

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

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

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

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.

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

Dimensionless Water Influx

Edge Water Drive

Idealized Radial Flow Model

2

310328.6et

Drc

ktt

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

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

Change in Boundary Pressure

Boundary Pressure Versus Time

Illustration of superposition concept

eDe pWBW

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

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

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 ?

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

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

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

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