SPE Distinguished Lecturer Program

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1 SPE Distinguished Lecturer Program The SPE Distinguished Lecturer Program is funded principally through a grant from the SPE Foundation. The society gratefully acknowledges the companies that support this program by allowing their professionals to participate as lecturers. Special thanks to the American Institute of Mining, Metallurgical, and Petroleum Engineers (AIME) for its contribution to the program. Society of Petroleum Engineers Distinguished Lecturer Program

2 Injectivity Impairment and Well & Water Management Prof. Pavel Bedrikovetsky Australian School of Petroleum, U of Adelaide PETROBRAS, Brazil Society of Petroleum Engineers Distinguished Lecturer Program 1

3 Contents Introduction 1. 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: IOR Conclusions 2

4 1. Formulation of the problem INJECTIVITY INDEX vs TOTAL WATER INJECTED II final / II inicial (%) Wi 10 3 m 3 water injected POÇO A POÇO B POÇO C POÇO D POÇO E POÇO F POÇO G POÇO H PÇO H_PDG Potência (PÇO H_PDG) Injectivity index II = q/δp decreased 10 times during 15-year waterflooding in giant offshore field (Campos Basin, Brazil) 3

5 Different physics mechanisms of retention 8

6 Water management cycle SURFACE TREATMENT ON-LINE MONITORING LOW BSW: DIRECTLY TO TERMINALS OIL (+WATER) SUB-SEA RAW WATER INJECTION PRODUCED WATER REINJECTION DISPOSAL IN SEA SUB-SEA OIL-WATER SEPARATION UNDERGROUND DISPOSAL DOWNHOLE OIL-WATER SEPARATION LOSS OF INJECTIVITY FRACTURE INJECTION AQUIFER OIL RESERVOIR OILY PARTICLE CONCENTRATION DUMP FLOODING NON-PRODUTION FORMATION 4

7 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

8 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

9 Filtration coefficient λ c σ σ t = (,U )Uc λ σ λ- particle capture probability per unit of its path; c - suspended concentrations; σ - retained concentrations; U - velocity 7

10 Formation damage coefficient β Darcy s law accounting for permeability damage k( σ) k 0 1 U=- k 0 μ 1+ βσ ( ) p 0 σ U velocity, σ - retained concentrations; k - permeability; μ - viscosity; p - pressure 9

11 Skin factor S characterises formation damage Δ μq R = + 2π k0 rw c p ln S Expression of impedance j via skin factor ( ) ( ) D ( D) ( ) D ( ) ( ) II 0 Δp t q 0 j( t D ) = = =1+ II t q t Δp 0 ( ) S td R ln r c w q - rate; R c drainage radius; r w well radius 10

12 Impedance (dimensionless pressure drop) grows linearly with time ( ) j t = 1+ mt D D ( ) m = φc β 1 e λ 0 L m impedance filtration growth coefficient Sharma et al., SPE 28489, 1994, SPE 38181, 1997, Ochi et al,

13 Transition time - deep bed filtration stops, - external cake formation starts, - retained particles fill α th fraction of porosity σ =αφ tr α critical porosity fraction Sharma et al., SPE 28489,

14 Mathematical model for external filter cake formation: particle balance in the cake accounting for cake porosity Darcy s law inside cake j( t ) = 1 + mt + m ( t t ) D Dtr c D Dtr k c 0 0 m c = k(1- c φc ) k c cake permeability, m c impedance cake growth coefficient Barkman, Davidson, JPT, 1972; M Sharma et al., SPE 28489, 1994, 38181, 1997; Z Khatib, SPE 28488, 1994, Ochi, 1998 φ 13

15 Stages of core / well impairment j(t ) D External cake development Cake erosion Deep bed filtration arctg m c 1 0 arctg m t Dtr t De t, p.v.i. D M Sharma et al., SPE 28489, 1994, 38181, 1997; Z Khatib, SPE 28488,

16 3. Erosion of external cake F e F p injected water F l l n Moment forces F and arms l: cf crossflow, g- gravity, p permeate, e electric, l- lifting, n normal, t - tangent reservoir cake l t F cf F g well Normal and tangent forces: F n =F p +F e -F l F t =F cf +F g F Civan, 2007, M Sharma et al., SPE 26323, 1993, Al-Abduwani et al.,

17 4. Accounting for oil-water mobility variation during waterflooding II(T) td, p.v.i. 17

18 Explanation Initial rise of injectivity due to displacement of more viscous oil by water 18

19 Combined Effect of Formation Damage and Mobility Variation ( ) j t D m j ( t ) + t, t < t M = m mc j ( t ) + t + ( t t ), t > t M M BL D D D Dtr BL D Dtr D Dtr D Dtr m impedance filtration growth coefficient; m c impedance filtration growth coefficient; j BL impedance decrease from Buckley-Leverett solution; M oil-water mobility ratio To monitor injectivity decline multiply initial II by M!! Bedrikovetsky, et al., SPE 88501, 90083,

20 Effect of waterflood on j-curve j(t ) D Impedance curves 1,2 and 3 for severe formation damage (M=1, 3 and 25); curves 4,5,6 low damage t, p.v.i D If II at the beginning of waterflood in heavy oil reservoir, and 2-4 months later, is the same -> expect injectivity decline soon!!! 20

21 5. Characterisation of injectivity damage system q(t) From Lab to Wells c(l,t) Δp(t) λ, β, α, k c, E r From Well History to Wells λ- filtration coefficient; β - formation damage coefficient; α - critical porosity fraction; k c cake permeability; E R erosion coefficient 21

22 3-point-pressure test to determine injectivity damage parameters 22

23 3-point-pressure test on the platform

24 Recalculation from core to well 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 23

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

26 SPIN: Simulation & Prediction of Injectivity t D (m³) J B Simulation Prediction of INjectivity (SPIN) Main Results J1 J2 J2T (m³) (d) (m³/s) (m³/s) Jc J J d S II Initial data V inj time V part Q dbf Rate R c (m) 500 P inj (Pa) E , ,868 0,037 0, , ,153 r w (m) 0,1 P res (Pa) , , ,64 0,043 0, ,742 1, ,348 H f (m) 30 K rwor 0,2 0, , ,623 0,039 0, ,826 1, ,211 H r (m) 15 K rowi 0,7 0, , ,613 0,035 0, ,917 1, ,09 λ (1/m) 1,9 S wi 0,2 0, , ,606 0,032 0, ,012 1, ,988 β 500 S or 0,25 0, , ,601 0,029 0, ,108 1, ,902 φ 0,2 n 3 0, ,72 0 0,596 0,026 0, ,205 2, ,83 k (m²) 4,E-12 m 1,3 0, , ,592 0,024 0, ,303 2, ,767 c 0 1E-06 C o (Btu/ft³.oF) 23 0, , ,589 0,023 0, ,401 2, ,714 ρ o (kg/l) 0,90 μ οi (Pa.s) 0,0072 0, ,548 0,0023 0,586 0,021 0,018 0,426 1,752 2, ,571 α 0,10 μ οi (Pa.s) 0,0072 0, ,75 0,0577 0,584 0,021 0,009 3,355 3,507 5, ,285 k c (m²) 5,E-16 C w (Btu/ft³.oF) 62,35 0, ,94 0,113 0,582 0,021 0,009 3,359 3,507 5, ,285 φc 0,6 ρ w (kg/l) 1,03 0, ,14 0,1684 0,58 0,021 0,009 3,363 3,507 5, ,285 r min (m) 3,0E-06 salinity (v/v) 0,1 0, ,35 0,2238 0,578 0,021 0,009 3,366 3,507 5, ,285 ρ c (kg/m³) 2450 C r (Btu/ft³.oF) 52,45 0, ,55 0,2792 0,576 0,021 0,009 3,369 3,507 5, ,285 T i ( o C) 82 ρ r (kg/l) 2,6 0, ,75 0,3345 0,574 0,021 0,009 3,372 3,507 5, ,285 T j ( o C) 20 E r 6 0, ,95 0,3899 0,573 0,022 0,009 3,375 3,507 5, ,285 Table for partial calculations of SPIN 0, ,15 0,4453 0,571 0,022 0,009 3,377 3,508 5, ,285 q initial (m³/s) 0, s2 0,55 0, ,41 0,5006 0,57 0,022 0,009 3,599 GOM (SHARMA,1994) 3,639 6, ,275 ΔP (Pa) D2 2,31 0, ,68 0,556 0,569 0,022 0,009 3,601 3,639 6, , Δρ (kg/m³) 1420 s3 0,748 0, ,2 0,6114 0,568 0,022 0,008 3,865 3,797 6,381 Sharma (sim SPIN prediction μ wi pure (Pa.s) 0,00036 D3 0,107 0, ,13 0 Observed 0,616 1,103 1,811 1 μ wj pure (Pa.s) 0,00100 s4 0,748 0, ,16 0 0,6 0,743 1, Simulated Modelling by commercial by SPE software μ wi (Pa.s) 0,00046 D4 0,052 0, ,34 0 0,591 0,714 1,205 1 μ wj (Pa.s) 0,00123 D2=t D; x D =1 0,432 0, ,44 0 0,585 0,969 1,64 1,1 μ οj (Pa.s) 0,03707 D3=t D; x D =1 9 0, ,15 0 0,58 1,091 1,85 1,1 6 M 1, D4=t D; x D =1 19 0, ,19 0 0,577 0,687 1,184 1,1 1/M 0, API 25,2 0, ,88 0 0, ,711 1,1 VP (m³) , ,42 0 0,573 1,16 1,978 1,2 `-h t 0,48 `-bt 13,03 0, ,17 0 0,573 1,399 2,375 1,2 Deep bed filtration m 4,E+01 0, ,18 0 0,573 1,486 2,522 1,3 3 out { } -7E-03 4ª exp -0, , ,3 0 0,572 1,783 3,017 1,3 x w 4,E-08 2ª exp 4,E+03 0, ,2 0,0112 0,572 2,309 3,895 1,3 2 Transition to external cake 0, ,47 0,0396 0,572 3,953 6,634 1,4 T Dtr 0, vol inj (m³) , ,16 0,069 0,571 2,967 4,993 1,4 Qtr (m³/s) 0, Jtr 3,E+00 0, ,28 0,0962 0,571 3,322 5,584 1,4 integral 1201,6155 vol. part. (m³) 0, , ,26 0,1202 0,571 2,865 4,823 1,5 1ª exp -1,067E-84 3ª exp 2,305E-88 0, ,12 0,1347 0,57 3,247 5,459 1,5 External cake 0, ,83 0,02 0,1538 0,57 0,04 0,06 3,1550,08 5,306 1,5 0,1 hmax (m) 2,975E-05 Je 1 0, ,52 0,1896 0,57 4,167 6,993t 1,6 D (pvi) hmin (m) 0 T De 0,043 0, ,32 0,2192 0,57 3,906 6,56 1,7 Jd Paiva, Bedrikovetsky, et al., SPE , 2006 SPE ,

27 Treatment of field data (Gulf of Mexico) by SPIN and by commercial simulator Column filling Cake erosion Cake formation Deep bed filtration 25

28 Treatment of raw well data, field case ( ) j t D m j ( t ) + t, t < t M = m m j t + t + t t M M BL D D D Dtr c ( ) ( ) BL D Dtr D Dtr Shumbera, D. A. et.al, 2003, SPE

29 Injectivity impairment parameters Frequency 45.00% 40.00% 35.00% 30.00% 25.00% 20.00% 15.00% 10.00% 5.00% 0.00% Lambda-3 3-point Point Lambda-Cor correlation Filtration coefficient, 1/m Filtration Lambda coefficient, (1/m) 1/m Formation damage coefficient Frequency 45.00% 40.00% 35.00% 30.00% 25.00% 20.00% 15.00% 10.00% 5.00% 0.00% Formation damage coefficient Beta Beta-3 3-point Point Beta-Cor correlation Well data Coreflood data 27

30 6. IOR & Waterflood management by fracture propagation Fractured injector: fracture propagation due to increasing leakage of untreated water and increasing formation damage; increase of areal sweep Unfavourable stress environment: low sweep Favourable stress environment: high sweep

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

32 Sweep improvement due to precipitation/sorption Injector Producer Water sweep front with skin Induced skin Low Permeability Zone High Permeability Zone Water sweep front without skin Polymer flooding adsorption of polymer CO 2 flooding precipitation of asphaltenes Cold waterflood of waxy oil - precipitation of paraffins

33 Injector Water sweep front with skin Producer Induced skin High Permeability Zone Water sweep front without skin 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 injectors Soo, Radke, (1999) less Sor Present work (2009) the same effect with horizontal wells

34 Minor effect of sweep increase at the very beginning of water injection With skin (0.1 p.v.i) Without skin (0.1 p.v.i) Water Small saturation difference can be observed near to injector in low permeable zone Oil

35 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) Water Oil P. Bedrikovetsky et al., 2009, SPE

36 Applications Implementation of damage option S(t D ) into waterflood simulators (IMEX, Eclipse) An accurate prediction of injectivity allows to plan well stimulation - fracturing, acidification, etc. 28

37 Filtration coefficient determines the size of the damaged zone 1 σ r d r = w + λ' -prediction of required perforation length to bypass the damage -calculation of required acid volume to remove damage P. Bedrikovetsky et al., 2009, SPE

38 Highly successful case field M-A (Equador) V acid 2 d = π r hφ

39 Applications 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 29

40 Conclusions 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 30

41 Collaborators: Acknowledgements 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) Thank you!!!