16. Courtesy: Jerauld et al., 2008. ⢠Application: oil recovery factor increases as injected water salinity decreases. ⢠Main mechanism: changing rock wettability.
Compositional Multiphase Relative Permeability Modeling for EOR processes
Mohammad R. Beygi, Mojdeh Delshad, and Mary F. Wheeler Center for Subsurface Modeling Institute for Computational Engineering and Sciences The University of Texas at Austin CSM Affiliate Meeting, Nov-04-2015
Motivation •
Mass-transfer intensive processes Hydrocarbon: miscible and near-miscible condition o Volatile oil/gas condensate fluids close to Pb /Pdew o Gasflood at enrichment/pressure slightly below MME/MMP o MCM gas injection: condensing/vaporizing gas drive
•
Brine-rock: low-salinity water flood Hydrocarbon-rock: Asphaltene precipitation Non hydrocarbon-brine-rock: CO2 sequestration and CO2-EOR
Limitation in modeling compositional processes Inaccurate results o Neglecting compositional effect (hydrocarbon/aqueous phase) o Low-saturation region
Numerical instability: Slow- or non- convergence (phase labeling?)
2
Outline • Miscible and near-miscible gas flood modeling • Low-salinity waterflood modeling • Contribution
3
Miscible/Near-Miscible Condition Relative Permeability Modeling
•
A) Viscous/gravitational assisted phase mobilization Capillary desaturation curve Capillary/trapping number
Phase Relative Permeability
Adding compositional effect to relative permeability:
Relative Permeability Parameter
1 0.9 0.8 0.7 0.6
0.5 0.4 0.3 0.2 0.1 0 1.E-08
1.E-06
1.E-04 1.E-02 Trapping Number
1.E+00
1.0 0.8 0.6 0.4
Inc. Nt
0.2 0.0 0
0.2
0.4
0.6
Phase Saturation
0.8
1 4
Miscible/Near-Miscible Condition Relative Permeability Modeling (cont’d) •
Compositional Inconsistency: Non-physical discontinuity in relative permeability (Phase labeling based on mass density)
•
B) Compositional consistent models Parachor-weighted molar density (Jerauld, 1997) Molar Gibbs free energy (Yuan and Pope, 2010)
Relative Permeability
1.2
𝑘𝑟𝑔
1 0.8
𝑘𝑟ℎ
0.6
𝑘𝑟𝑜
0.4 0.2 0 0
50
100
150
Block Number
200
5
𝑘𝑟,ℎ = 𝑓 Fℎ 𝐹ℎ = 𝑓(Gℎ )
Relative Permeability Parameter
Kr(GFE) Application (Yuan and Pope, 2010) 𝐹2𝑅 𝑭𝒉 𝐹3𝑅
𝐹1𝑅 𝐺1𝑅
𝐺2𝑅 𝑮𝒉 𝐺3𝑅 Molar GFE
Partly introduces compositional consistency but is incomplete 6
Complete Kr(GFE) Application (Current Issues) Components: C1/C4/nC10, Zi=0.6/0.2/0.2, T=280℉ Phase-2
•
Single phase
GFE non-monotonicity Phase-1
•
Implementation to multiphase flow Dissimilar effect of composition on two-phase rel. perm. parameters 0 0 (𝑘𝑟𝑗𝑙 𝑎𝑛𝑑 𝑘𝑟𝑗𝑚 , 𝐶1𝑗𝑙 𝑎𝑛𝑑 𝐶1𝑗𝑚 , …)
𝐹3𝑅
𝐹2𝑅 𝐹1𝑅 𝐺1𝑅
𝐺2𝑅
𝐺3𝑅
6
Complete GFE Application (Background) 𝐺 = 𝐺 𝛼 + 𝐺𝛽 + 𝐺 𝑠 + 𝜎𝐴
𝜕𝐺 𝜎= 𝜕𝐴
Gibbs ideal interface
β P,T,n
σ
Guggenheim model
β S
α
α 8
Complete GFE Application 𝑘𝑟𝑗 = 𝑓 𝐹𝑗3𝑃
𝐹𝑗3𝑃 = 𝑓 𝐹𝑗𝑖
𝑭𝒋𝒊 𝑅 𝐹23
𝐹𝑗𝑖 = 𝑓 𝐺𝐹𝐸𝑗 , 𝜎 𝐺𝐹𝐸 𝑗𝑖 𝑆
𝑅 𝐹32 𝑅 𝐹13 𝑅 𝐹31
Two-phase parameters: Use bilinear GFE-IFT-weighted interpolation scheme
𝑅 𝐹21 𝑅 𝐹12 𝑅 𝜎23
𝑅 𝜎12
𝐺1𝑅
𝐺2𝑅
𝐺3𝑅
𝑮𝒋
𝑅 𝜎13
𝝈𝒋𝒊 9
Miscible/Near-Miscible Gas-flood Rel. Perm. Modeling Compositional UTKR3P model (Beygi et al., 2013) 𝑘𝑟,ℎ = 𝑓 Fℎ 𝐹ℎ = 𝑓(Fℎ,𝑙 , Fℎ,𝑘 )
Parameter set: 𝑟𝑒𝑓 ° P, T, X, Gh , σh,n , Fℎ,𝑛
𝐹ℎ,𝑛 = 𝑓(Gh , σh,n ) Gh = 𝑓(Gℎ𝑖 ) ° 𝐺ℎ𝑖 = 𝑓(P, T, xi , Ghi ) ° Ghi = 𝑓(P, T, 𝐶𝑝𝑖 )
10
Case-study: CO2/C1/FC6 (T=260℉, P=1750 psi) Single HC phase in composition space Z3 mole fraction in single HC phase
Saturation space
*: Gaseous phase *: Oleic phase
Z1 mole fraction in single HC phase
11
Case-study: CO2/C1/FC6 (T=260℉, P=1750 psi) (cont’d) Two-phase HC in composition Space
Iso-GFE in composition Space
12
Case-study: CO2/C1/FC6 Single Hydrocarbon Phase Relative Permeability Hydrocarbon Saturation=0.9 Gibbs Free Energy
Phase Labeling 0.8
0.2
GFE modeling results in continuous relative permeability
13
Case-study: CO2/C1/FC6 Two Hydrocarbon Phase Region:Phase-1 Relative Permeability
Complete compositional relative permeability based on GFE modeling
14
Outline • Miscible and near-miscible gas flood modeling • Low-salinity waterflood modeling • Contribution
15
Low-Salinity Waterflood (Background)
• Application: oil recovery factor increases as injected water salinity decreases
∆𝑹𝑭
• Main mechanism: changing rock wettability
• Implication: 𝑘𝑟𝑤 ↓ and 𝑘𝑟𝑜𝑤 ↑
Courtesy: Jerauld et al., 2008
16
Low-Salinity Waterflood (Background)
Wettability Alteration Mechanism • Sandstone Rock Clay Content Oil wet surface: Electrical Double Layer Wettability alteration toward increased water wetness o Low-Sal expands EDL
• Carbonate Rock Calcite dissolution
Courtesy: Lee et al., 2010
Courtesy: Hiorth et al., 2010 17
Low-Salinity Waterflood (Background)
Rel. Perm. Modeling 𝐻𝑆 ∗ 𝐿𝑆 ∗ 𝑘𝑟𝑗 = 𝜃𝑘𝑟𝑗 𝑆 + (1 − 𝜃)𝑘𝑟𝑗 𝑆
𝜃 =f() 𝐿𝑆 𝑘𝑟𝑜𝑤
Sorw TDS
Omekeh et al. (2012)
Divalent cation desorption
Korrani (2014) Sandsone
Total Ionic strength
Korrani (2014) Carbonate
Calcite content
Dang et al. (2013)
Exchange capacity of clays
Wu and Bai (2009): Sorw = 𝑓(Salinity)
Relative Permeability
Jerauld et al. (2008)
𝐻𝑆 𝑘𝑟𝑜𝑤
𝐻𝑆 𝑘𝑟𝑤 𝐿𝑆 𝑘𝑟𝑤
Water Saturation
18
Low-Salinity Waterflood GFE-Wettability Contact Angle (Degree)
Wettability= f(contact angle) 100 95 90 85 80 75 70 65 60
Contact angle=f(GFE)
Sea water (HS)
Dilution × 100
1st Coreflood 2nd Coreflood
-200
Low. Sal
-150
-100 Molar GFE (kJ/mol)
-50
Yousef et al. (2011) experiments on carbonate rocks, (Courtesy: Alshalabi, 2014)
0 19
Low-Salinity Waterflood Rel. Perm. Modeling 𝑘𝑟,𝑎𝑞 = 𝑓 F𝑎𝑞 (UTKR3P model) 𝐹𝑎𝑞 = 𝑓(F𝑎𝑞,𝑙 , F𝑎𝑞,𝑘 ) 𝐹𝑎𝑞,𝑛 = 𝑓(Gaq , σaq,n )
Gaq = 𝑓(G𝑊𝑖 )
Parameter set: 𝑟𝑒𝑓 ∗ ,σ P, T, W, Gaq , F aq,n ℎ,𝑛 , Brine(rock) composition UT-PGE bridge model: Petrophysic- GeochemistryElectrolyte thermodynamic
∗ 𝐺𝑊𝑖 = 𝑓(P, T, m𝑖 , γ𝑖 , G𝑊𝑖 )
γi : Appropriate Activity model {Batch reaction simulation results (PHREEQC®) or a general purpose in-house code}
20
Modified Salinity Case Study Water analysis for South American formation, Kazempour et al., 2013 Ions
High Salinity (ppm)
Low Salinity (ppm)
Na+
2430
40
1
K+
66
