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Society of Petroleum Engineers Distinguished Lecturer Programwww.spe.org/dl

Injectivity Impairment and Well & Water Management

Prof. Pavel Bedrikovetsky

Australian School of Petroleum, U of Adelaide

PETROBRAS, Brazil

Society of Petroleum Engineers Distinguished Lecturer Programwww.spe.org/dl

1

ContentsIntroduction1. Formulation of the problem

2. Deep bed filtration & External filter cake formation

3. Erosion of external cake

4. Early effect of varying oil-water mobility ratio

5. Damage characterisation and prediction

6. Taking advantage of formation damage: IORConclusions

2

Injectivity index II = q/Δp decreased 10 times during 15-year waterflooding in giant offshore field

(Campos Basin, Brazil)

INJECTIVITY INDEX vs TOTAL WATER INJECTED

0102030405060708090

100

0 500 1000 1500 2000 2500 3000Wi

II fin

al / I

I inic

ial

(%)

POÇO A POÇO B POÇO CPOÇO D POÇO E POÇO FPOÇO G POÇO H PÇO H_ PD GPo t ência ( PÇO H_ PD G)

1. Formulation of the problem

103 m3 water injected

3

Different physics mechanisms of retention

8

OIL RESERVOIR

NON-PRODUTION FORMATION

OIL (+WATER)

SURFACE TREATMENT

FRACTURE INJECTION

LOSS OF INJECTIVITY

SUB-SEA RAW WATER INJECTION

DOWNHOLE OIL-WATER

SEPARATION

SUB-SEA OIL-WATER SEPARATION

UNDERGROUND DISPOSAL

DUMP FLOODING

ON-LINE MONITORING

LOW BSW: DIRECTLY TO TERMINALS

PRODUCED WATER

REINJECTION

DISPOSAL IN SEA

Water management cycle

AQUIFER OILY PARTICLE CONCENTRATION

4

What can you do about injectivity decline

• Water filtering: filter choice?

• Chemical treatment: what type of chemical?

• Acidizing: when? acid volume?

• Fracturing: when?

• Add perforation holes: when? size?

Decisions !!!

Decisions !!!

5

2. Deep bed filtration and external cake formation

Particles filtrate deep into formation, fill in the inlet, stop filtration and form external filter cake

6

Filtration coefficient λ

λ- particle capture probability per unit of its path; c - suspended concentrations; σ - retained concentrations; U - velocity

cσ

( ,U )Uctσ λ σ∂

=∂

7

Darcy’s law accounting for permeability

damage

( )∇0kU = - p

μ 1+ βσ

1

0 σ

k( )σk0

Formation damage coefficient β

U – velocity, σ - retained concentrations; k - permeability; μ - viscosity; p - pressure

9

( ) ( )( )

( )( )

( )( )

( )D DD

cD D

w

Δp t S tII 0 q 0j t = = = 1+ RII t q t Δp 0 ln

r

c

0 w

Rqp ln S2 k rμΔπ

⎛ ⎞= +⎜ ⎟

⎝ ⎠

Skin factor S characterises formation damage

Expression of impedance j via skin factor

q - rate; Rc – drainage radius; rw – well radius 10

( )D Dj t 1 mt= +

( )0 Lm c 1 e λφ β −= −

Impedance (dimensionless pressure drop) grows linearly with time

m – impedance filtration growth coefficientSharma et al., SPE 28489, 1994, SPE 38181, 1997, Ochi et al, 1998 11

φασ =tr

Transition time

α– critical porosity fraction

- deep bed filtration stops, - external cake formation starts,- retained particles fill α–th fraction of porosity

12Sharma et al., SPE 28489, 1994

•particle balance in the cake accounting for cake porosity

•Darcy’s law inside cake

Barkman, Davidson, JPT, 1972; M Sharma et al., SPE 28489, 1994, 38181, 1997; Z Khatib, SPE 28488, 1994, Ochi, 1998

( ) 1 ( )D Dtr c D Dtrj t m t m t t= + + −

00

cc c

k cm =

k (1 - )φφ

Mathematical model for external filter cake formation:

kc – cake permeability, mc –impedance cake growth coefficient

13

Stages of core / well impairment

M Sharma et al., SPE 28489, 1994, 38181, 1997; Z Khatib, SPE 28488, 1994

01

j(t )DExternal cakedevelopment Cake erosion

Deep bedfiltration

t , p.v.i.D

arctg mc

arctg m

tDtr tDe

14

3. Erosion of external cakeMoment forces F and arms l:

cf – crossflow, g- gravity,

p – permeate, e – electric,

l- lifting, n – normal, t - tangentln

lt

Fe

Fp

Fgreservoircake well

injected water

Fl

Fcf

Fn=Fp+Fe-FlFt=Fcf+Fg

F Civan, 2007, M Sharma et al., SPE 26323, 1993, Al-Abduwani et al., 2005 15

Normal and tangent forces:

4. Accounting for oil-water mobility variation during waterflooding

0.0

20.0

40.0

60.0

80.0

100.0

120.0

140.0

0 0.02 0.04 0.06 0.08

tD, p.v.i.

II(T)

17

Initial rise of injectivity due to displacement of more viscous oil by water

Explanation

18

Combined Effect of Formation Damage and Mobility Variation

( )( )

( ) ( )

,

,

BL D D D Dtr

Dc

BL D Dtr D Dtr D Dtr

mj t t t tMj t

mmj t t t t t tM M

⎧ + <⎪⎪= ⎨⎪ + + − >⎪⎩

m – impedance filtration growth coefficient; mc – impedance filtration growth coefficient; jBL – impedance decrease from Buckley-Leverett solution;

M – oil-water mobility ratio

To monitor injectivity decline – multiply initial II by M !!

19Bedrikovetsky, et al., SPE 88501, 90083, 93885

Impedance curves 1,2 and 3 for severe formation damage (M=1, 3 and 25); curves 4,5,6 – low damage

If II at the beginning of waterflood in heavy oil reservoir, and 2-4 months later, is the same -> expect injectivity decline soon!!!

Effect of waterflood on j-curve

12 3

4

56

1.0

t , p.v.i.D

j(t )D

0 0.007 0.014

20

Δp(t)q(t)

c(L,t)

λ, β, α, kc,

Er

From Lab to Wells

From Well History to Wells

5. Characterisation of injectivity damage system

λ- filtration coefficient; β - formation damage coefficient; α - critical porosity fraction; kc – cake permeability;ER – erosion coefficient 21

3-point-pressure test to determine injectivity damage parameters

22

3-point-pressure test on the platform

Recalculation from core to well

23

•Vertical well:axi symmetric flow

•Horizontal injector:rate/damage distribution along the well

•Fractured injector:almost linear geometry, fracture growth

•Perforated injector:holes filling instead of cake formation

Set-up for the 3-point-pressure test mounted on a sea platform

Simulation Prediction of INjectivity (SPIN) Main Results

Initial data tDVinj

(m³)time (d)

Vpart

(m³) JB

Qdbf

(m³/s)Rate (m³/s) Jc J Jd S II

Rc (m) 500 Pinj (Pa) 29000000 1E-06 5 0,0015 0 0,868 0,037 0,037 0 0,868 1 28 1,153

rw (m) 0,1 Pres (Pa) 27000000 0,005 22153 5,9647 0 0,64 0,043 0,043 0 0,742 1,169 23 1,348

Hf (m) 30 Krwor 0,2 0,009 44301 12,605 0 0,623 0,039 0,039 0 0,826 1,338 27 1,211

Hr (m) 15 Krowi 0,7 0,014 66449 19,982 0 0,613 0,035 0,035 0 0,917 1,507 31 1,09

λ (1/m) 1,9 Swi 0,2 0,019 88598 28,119 0 0,606 0,032 0,032 0 1,012 1,677 35 0,988

β 500 Sor 0,25 0,024 110746 37,029 0 0,601 0,029 0,029 0 1,108 1,846 39 0,902

φ 0,2 n 3 0,028 132894 46,72 0 0,596 0,026 0,026 0 1,205 2,015 43 0,83

k (m²) 4,E-12 m 1,3 0,033 155042 57,197 0 0,592 0,024 0,024 0 1,303 2,184 47 0,767

c0 1E-06 Co (Btu/ft³.oF) 23 0,038 177191 68,465 0 0,589 0,023 0,023 0 1,401 2,353 51 0,714

ρ o (kg/l) 0,90 μο i (Pa.s) 0,0072 0,042 199339 82,548 0,0023 0,586 0,021 0,018 0,426 1,752 2,941 66 0,571

α 0,10 μο i (Pa.s) 0,0072 0,047 221487 110,75 0,0577 0,584 0,021 0,009 3,355 3,507 5,871 141 0,285

kc (m²) 5,E-16 Cw (Btu/ft³.oF) 62,35 0,052 243635 138,94 0,113 0,582 0,021 0,009 3,359 3,507 5,874 141 0,285

φc 0,6 ρ w (kg/l) 1,03 0,056 265783 167,14 0,1684 0,58 0,021 0,009 3,363 3,507 5,878 141 0,285

rmin (m) 3,0E-06 salinity (v/v) 0,1 0,061 287932 195,35 0,2238 0,578 0,021 0,009 3,366 3,507 5,882 141 0,285

ρ c (kg/m³) 2450 Cr (Btu/ft³.oF) 52,45 0,066 310080 223,55 0,2792 0,576 0,021 0,009 3,369 3,507 5,885 141 0,285

Ti (oC) 82 ρ r (kg/l) 2,6 0,071 332228 251,75 0,3345 0,574 0,021 0,009 3,372 3,507 5,887 141 0,285

Tj (oC) 20 Er 6 0,075 354376 279,95 0,3899 0,573 0,022 0,009 3,375 3,507 5,89 141 0,285Table for partial calculations of SPIN 0,08 376525 308,15 0,4453 0,571 0,022 0,009 3,377 3,508 5,892 141 0,285q initial (m³/s) 0,0318818 s2 0,55 0,085 398673 337,41 0,5006 0,57 0,022 0,009 3,599 3,639 6,114 146 0,275

ΔP (Pa) 2000000 D2 2,31 0,089 420821 366,68 0,556 0,569 0,022 0,009 3,601 3,639 6,117 146 0,275

Δρ (kg/m³) 1420 s3 0,748 0,094 442969 397,2 0,6114 0,568 0,022 0,008 3,865 3,797 6,381 Sharma (sim

μwi pure (Pa.s) 0,00036 D3 0,107 0,00 15551 226,13 0 0,616 1,103 1,811 1

μwj pure (Pa.s) 0,00100 s4 0,748 0,008 37901 232,16 0 0,6 0,743 1,239 1

μwi (Pa.s) 0,00046 D4 0,052 0,013 61766 238,34 0 0,591 0,714 1,205 1

μwj (Pa.s) 0,00123 D2=tD; xD=1 0,432 0,017 81962 245,44 0 0,585 0,969 1,64 1,1

μο j (Pa.s) 0,03707 D3=tD; xD=1 9 0,021 98893 252,15 0 0,58 1,091 1,85 1,1

M 1,6662533 D4=tD; xD=1 19 0,024 115083 256,19 0 0,577 0,687 1,184 1,1

1/M 0,6001488 API 25,2 0,028 130769 261,88 0 0,573 1 1,711 1,1

VP (m³) 4712389 0,031 143930 267,42 0 0,573 1,16 1,978 1,2

`-ht 0,48 `-bt 13,03 0,035 163116 277,17 0 0,573 1,399 2,375 1,2

Deep bed filtration m 4,E+01 0,037 174257 283,18 0 0,573 1,486 2,522 1,3out { } -7E-03 4ª exp -0,00087 0,04 189909 293,3 0 0,572 1,783 3,017 1,3

xw 4,E-08 2ª exp 4,E+03 0,043 202902 304,2 0,0112 0,572 2,309 3,895 1,3Transition to external cake 0,045 214245 320,47 0,0396 0,572 3,953 6,634 1,4

TDtr 0,0421053 vol inj (m³) 198416 0,048 226026 333,16 0,069 0,571 2,967 4,993 1,4Qtr (m³/s) 0,0126752 Jtr 3,E+00 0,05 236899 346,28 0,0962 0,571 3,322 5,584 1,4integral 1201,6155 vol. part. (m³) 0,4960409 0,052 246492 356,26 0,1202 0,571 2,865 4,823 1,51ª exp -1,067E-84 3ª exp 2,305E-88 0,054 252315 363,12 0,1347 0,57 3,247 5,459 1,5

External cake 0,055 259922 371,83 0,1538 0,57 3,155 5,306 1,5hmax (m) 2,975E-05 Je 1 0,058 274261 393,52 0,1896 0,57 4,167 6,993 1,6hmin (m) 0 TDe 0,043 0,061 286109 410,32 0,2192 0,57 3,906 6,56 1,7

GOM (SHARMA,1994)

0

1

2

3

4

5

6

7

8

9

10

0 0,02 0,04 0,06 0,08 0,1tD (pvi)

J d

SPIN predictionObservedSimulated by SPE 28429

J2 J2TJ1

Modelling by commercial software

Paiva, Bedrikovetsky, et al., SPE 100334, 2006SPE 107866, 2007

SPIN: Simulation & Prediction of Injectivity

24

Column filling

Cake erosion

Deep bed filtration

Cake formation

Treatment of field data (Gulf of Mexico) by SPIN and by commercial simulator

25

Shumbera, D. A. et.al, 2003, SPE 84416

Treatment of raw well data, field case

( )( )

( ) ( )

,BL D D D Dtr

Dc

BL D Dtr D Dtr

mj t t t tMj t

mmj t t t tM M

⎧ + <⎪⎪= ⎨⎪ + + −⎪⎩

26

0.00%5.00%

10.00%15.00%20.00%25.00%30.00%35.00%40.00%45.00%

10 30 60 90 120

150

180

210

240

270

300

Lambda (1/m)

Freq

uenc

y

Lambda-3 PointLambda-Cor

Injectivity impairment parameters

Well data Coreflood data

Formation damage coefficient

0.00%5.00%

10.00%15.00%20.00%25.00%30.00%35.00%40.00%45.00%

200 400 600 800 1000 1200 1400 1600

Beta

Freq

uenc

yBeta-3 PointBeta-Cor

Formation damage coefficient

Filtration coefficient, 1/m Filtration coefficient, 1/m

3-point

correlation

3-point

correlation

27

Fractured injector: fracture propagation

due to increasing leakage of untreated water and increasing formation damage; increase of areal

sweep

6. IOR & Waterflood management by fracture propagation

Unfavourable stress environment: low sweep

Favourable stress environment: high sweep

Perforation density along the column :

N(x) = ?

Non-uniformal perforation homogenizes injectivity profile and increases sweep efficiency

Injectivity damage also homogenizes injectivity profile and increases sweep for any “unpredictable” heterogeneity

P. Dore, P. Bedrikovetsky et al., 2005, SPE 99343

Injector Producer Sweep increase due to formation damage and non-uniform perforation

Sweep improvement due to precipitation/sorption

High Permeability Zone

Injector Producer

Water sweep front without skin

Water sweep front with skin

Induced skin Low

Permeability Zone

Polymer flooding –adsorption of polymer CO2 flooding – precipitation of asphaltenesCold waterflood of waxy oil - precipitation of paraffins

Idea of oil recovery increase by injection of water with particles: The damage is high where the injection rate is high, i.e. the injectivity profile becomes more uniform and sweep efficiency increases

Khambharatana, Faruq Ali et al. (1998) – poor sweep increase with vertical injectorsSoo, Radke, (1999) – less SorPresent work (2009) – the same effect with horizontal wells

High Permeability Zone

Injector Producer

Water sweep front without skin

Water sweep front with skin

Induced skin

Minor effect of sweep increase at the very beginning of water injection

Water Oil

With skin (0.1 p.v.i) Without skin (0.1 p.v.i)

Small saturation difference can be observed near to injector in low permeable zone

Water Oil

Skin results in high increase of the final sweep from low permeability zone

With skin (2.0 p.v.i) Without skin (2.0 p.v.i)

P. Bedrikovetsky et al., 2009, SPE 122843

Implementation of damage option S(tD) into waterflood simulators (IMEX, Eclipse)

An accurate prediction of injectivity allows to plan well stimulation - fracturing, acidification, etc.

Applications

28

Filtration coefficient determines the size of the damaged zone

-prediction of required perforation length to bypass the damage-calculation of required acid volume to remove damage

'1λ

σ += wd rr

P. Bedrikovetsky et al., 2009, SPE 122844

Highly successful case – field M-A (Equador)

2acid dV r hπ φ=

Database of injectivity damage parameters from lab tests and well history

Prediction of injector behaviour for “new” fields, not yet submitted to waterflooding, based on basic data on permeability, porosity, pore size distribution

The developed theory can be applied for •drilling-fluid-invasion-induced formation damage, •fines migration and damage of producers, •gravel pack impairment, •sand screen design

Applications

29

Theory for well injectivity impairment shows

•Good match with field data

•Good match with laboratory tests

3-point-pressure tool characterises injectivity damage system and is used in field / platform conditions

Mathematical model is implemented in software SPIN

Database of damage parameters –> for injectivity prediction

Conclusions

30

Collaborators:

•A L Serra de Souza, C A Furtado, P Dore, A G Siqueira, F Shecaira(Petrobras, Cenpes)

•R Paiva, A Santos, M da Silva, Maylton F da Silva, A C Gomes, E Resende

(UENF-Lenep / Petrobras)

•F Al-Abduwani, P Currie, W. Van den Broek,(Delft University of Technology, The Netherlands)

•D Marchesin, G Hime, A Alvares (IMPA, Brazil)

•A Shapiro (Technical University of Denmark)

•O Dinariev (Russian Academy of Sciences)

Acknowledgements

Thank you !!!