investigation of compositional grading in petroleum...
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RESERVOIR SIMULATION
Investigation of Compositional Grading in
Petroleum Reservoirs
Zhangxing Chen
University of Calgary
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Outline • Importance of the Research • Factors Leading to
Compositional Variations • Compositional Grading • Theory • Numerical Experiments • Conclusions
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Importance of the Research
• Initialization of simulation:
- Mechanical equilibrium - Chemical equilibrium
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Importance of the Research (cont’d)
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Importance of the Research (cont’d)
• Accurate modeling of composition variation highly affects:
- Reserve estimation - Design of production and
development strategies
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Factors Leading to Composition Variation
• Gravity: gravity segregation.
• Thermal diffusion: light components to warm zones and heavy ones to cold zones.
• Incomplete hydrocarbon migration/mixing: complete mixing takes time.
• Natural convection: leading to an increase of horizontal compositional variation.
• Dynamic flux of water aquifer contacting only a part of reservoir: creating a sink for continuous depletion of light components (e.g., methane)
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Factors Leading to Composition Variation (cont’d)
• Asphaltene precipitation during migration: leading to different layers with different permeability to host different types of oil.
• Biodegradation varying laterally and vertically: causing significant variation in H2S content and API gravity of the reservoir.
• Reservoir compartmentalization: causing loss of pressure and fluid communication between adjacent fault blocks.
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Factors Leading to Composition Variation (cont’d)
• Partial barriers: causing limited fluid and pressure communication.
• Genesis: related to source rocks. • Capillary forces: having an effect on fluid
distribution in systems with pore radius in the order of 1 micron.
• Artificial issues: e.g., miscible gas injection
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Processes and Time Scales Affecting Fluid Compositions
• Multiple processes that affect fluid properties: – Reservoir charge/filling, fluid mixing through Darcy flow/advection/
diffusion, gravity segregation, biodegradation, fractionation, and differential leakage of gas vs. oil.
• Different time scales (key to understanding the relative significance of fluid data to reservoir segmentation studies): – Charge/filling of reservoirs: geological time - several millions of
years – Biodegradation: thousands to hundreds of thousand of years – Molecular diffusion: 1 to 100 million years – Pressure diffusion: hundreds or even thousands of years – Convective flow: thousands to million years
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Importance of the Research (cont’d): Understanding Reservoir Fluid Compositions
Time scale
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Difficulties in Modeling Compositional Variation
• We do not have enough physical/chemical understanding of these phenomena.
• Boundary conditions are changing continually.
• Mathematical models may be so complex or even unknown.
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Compositional Grading
• Gravity • Thermal diffusion (Soret
effect) • Capillary effects
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Theory
• Classical theory • New general theory
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Classical Theory
• Constraint of chemical equilibrium for an isothermal system (Gibbs, 1876):
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Classical Theory (cont’d)
• Constraint of chemical equilibrium for a nonisothermal system (Faissat, et al., 1994):
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New General Theory
• Mass conservation
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New General Theory (cont’d)
• Diffusive mass flux:
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Relationship between classical and new theories
• For an isothermal system, the classical constraint of chemical equilibrium can be obtained from the pressure diffusion.
• For a non isothermal system, it can be obtained from the thermal diffusion.
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Simulation Approach • R&D Program: Have developed a software package that
integrates geological processes (source rock maturation, hydrocarbon generation, migration, charge/filling, etc.) with reservoir processes (fluid mixing, advection, diffusion, gravity segregation, biodegradation, etc.).
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Case Study A: A Light Oil
• A North Sea reservoir • The thickness of reservoir: 200m • Reference pressure and temperature
at 3,000m: 40 MPa and 320 K • Temperature gradient: 0.02 K/m • Components: C1--C10+
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Case Study A (cont’d) Depth (m) 3000 3050 3100 3150 3200
C1 % 68.861 63.6557 60.1561 57.4384 55.2189
C10+ % 5.231 8.9845 11.9898 14.5655 16.8147
P (MPa) 40 40.252 40.528 40.820 41.122
dens (kg/m3) 478.28 542.57 580.50 606.88 626.49
Pb (MPa) 35.474 31.862 29.520 27.539 25.892
Rs (Sm3/Sm3) 1132.5 655.1 482.5 389.5 330.7
Bo (m3/Sm3) 3.962 2.665 2.208 1.966 1.815
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Case Study A (cont’d)
Pref (bar) Tref (K) Error OIP %
320 400 39.77
336.79 395.0175 44.47
353.58 390.035 48.75
370.37 385.0525 52.73
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Case Study B: A Black Oil Two-Phase
• Location: the Azadegan oil, southwest of Iran.
• Components: C1—C7+ • Temperature gradient: 0.01 K/m,
which is normally considered isothermal.
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Case Study B (cont’d)
Depth (m) 3000 2950 2900 2850 2800 C1 % 36.47 72.4079 74.2365 75.6161 76.7778 C7+ % 33.29 0.7870 0.4672 0.3052 0.2093 P (bar) 240.000 237.136 236.198 235.310 234.455
Dens (kg/m3) 654.72 198.37 185.41 177.33 171.41 Pb (bar) 194.102 - - - - Pd (bar) - 233.482 191.729 156.929 124.729
Rs (Sm3/Sm3) 152.880 - - - - Bo (m3/Sm3) 1.541 - - - -
T (K) 400 400 399 399 398 MW of C7+ 218 209.13 201.84 195.28 189.33
GOC depth (m) 2955 - - - -
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Case Study B (cont’d)
Condition
Without Plus Fraction
Change with Depth
Isothermal
Error OIP% 31.18 39.33
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Case Study C: Single Phase
• Location: the Azadegan oil, southwest of Iran.
• 12 Components: H2S, N2, CO2, C1, C2, C3, iC4, nC4, iC5, nC5, C6, C7+
• Reference pressure and temperature at 3,000m: 175 Bar and 370 K
• Temperature gradients in x, y, and z directions: 0.003, 0.004, -0.035 K/m.
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Case Study C (cont’d) Component Mole% H2S 0.04 N2 0.4 CO2 1.44 C1 29.59 C2 7.36 C3 5.39 iC4 0.91 nC4 2.98 iC5 1.43 nC5 1.78 C6 1.4 C7+ 47.28
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Case Study C (cont’d)
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Case Study D: Analytical Solution
yr
yr
yr
yr
yr
yr
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Case Study E: Diffusive Mixing
0 0.5 1
2 myr
80 myr
20 myr
400 myr
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Case Study F: n-Component
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Case Study G: Rayleigh Number
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Case Study H: Reservoir with Baffle for n-Component Mixing
nC4 mole fraction
C1 mole fraction
Kx = 100 md in reservoir Kx = 10, 1, 0.1, 0.0001 md in baffle
Kz = 10 md in reservoir Kz = 1/10 of Kx in baffle
Pressure gradient (atm)
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Case Study H: Reservoir with Baffle for n-Component Mixing (cont’d)
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Case Study I: Effect of Pressure and Thermal Diffusions
Equilibrium at t = 19 million years with pressure and thermal diffusions
Equilibrium at t = 17 million years with pressure diffusion
Equilibrium at t = 20 million years with thermal diffusion
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Conclusions • The effect of compositional grading is magnificent and cannot
be ignored; its effect is more pronounced as the fluid becomes near-critical.
• Ignoring change in composition can lead to huge errors in OIP calculations as much as 50% of the real number.
• The temperature gradient must be included in calculations as it has a remarkable effect on compositional grading and the change of physical properties with depth.
• Molecular weight and so all other properties of the plus fraction can change with depth, which cannot be ignored.
• Gravity causes the fluid and the plus fraction to become heavier towards the bottom while the temperature gradient does the opposite.
• Pressure equilibration seems fastest.