Investigation of Compositional Grading in Petroleum Reservoirs Zhangxing Chen University of Calgary
Outline Importance of the Research Factors Leading to Compositional Variations Compositional Grading Theory Numerical Experiments Conclusions
Importance of the Research Initialization of simulation: - Mechanical equilibrium - Chemical equilibrium
Importance of the Research (cont d)
Importance of the Research (cont d) Accurate modeling of composition variation highly affects: - Reserve estimation - Design of production and development strategies
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)
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 H 2 S content and API gravity of the reservoir. Reservoir compartmentalization: causing loss of pressure and fluid communication between adjacent fault blocks.
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
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
Importance of the Research (cont d): Understanding Reservoir Fluid Compositions Time scale
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.
Compositional Grading Gravity Thermal diffusion (Soret effect) Capillary effects
Theory Classical theory New general theory
Classical Theory Constraint of chemical equilibrium for an isothermal system (Gibbs, 1876):
Classical Theory (cont d) Constraint of chemical equilibrium for a nonisothermal system (Faissat, et al., 1994):
New General Theory Mass conservation
New General Theory (cont d) Diffusive mass flux:
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.
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.).
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: C 1 --C 10+
Case Study A (cont d) Depth (m) 3000 3050 3100 3150 3200 C 1 % 68.861 63.6557 60.1561 57.4384 55.2189 C 10+ % 5.231 8.9845 11.9898 14.5655 16.8147 P (MPa) 40 40.252 40.528 40.820 41.122 dens (kg/ m 3 ) 478.28 542.57 580.50 606.88 626.49 P b (MPa) 35.474 31.862 29.520 27.539 25.892 R s (Sm 3 / Sm 3 ) 1132.5 655.1 482.5 389.5 330.7 B o (m 3 /Sm 3 ) 3.962 2.665 2.208 1.966 1.815
Case Study A (cont d) P ref (bar) T ref (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
Case Study B: A Black Oil Two-Phase Location: the Azadegan oil, southwest of Iran. Components: C 1 C 7+ Temperature gradient: 0.01 K/m, which is normally considered isothermal.
Case Study B (cont d) Depth (m) 3000 2950 2900 2850 2800 C 1 % 36.47 72.4079 74.2365 75.6161 76.7778 C 7+ % 33.29 0.7870 0.4672 0.3052 0.2093 P (bar) 240.000 237.136 236.198 235.310 234.455 Dens (kg/m 3 ) 654.72 198.37 185.41 177.33 171.41 P b (bar) 194.102 - - - - P d (bar) - 233.482 191.729 156.929 124.729 R s (Sm 3 /Sm 3 ) 152.880 - - - - B o (m 3 /Sm 3 ) 1.541 - - - - T (K) 400 400 399 399 398 MW of C 7+ 218 209.13 201.84 195.28 189.33 GOC depth (m) 2955 - - - -
Case Study B (cont d) Condition Error OIP % Without Plus Fraction Change with Depth Isothermal 31.18 39.33
Case Study C: Single Phase Location: the Azadegan oil, southwest of Iran. 12 Components: H 2 S, N 2, CO 2, C 1, C 2, C 3, ic 4, nc 4, ic 5, nc 5, C 6, C 7+ 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.
Case Study C (cont d) Component Mole% H 2 S 0.04 N 2 0.4 CO 2 1.44 C 1 29.59 C 2 7.36 C3 5.39 ic 4 0.91 nc 4 2.98 ic 5 1.43 nc 5 1.78 C 6 1.4 C 7+ 47.28
Case Study C (cont d)
Case Study D: Analytical Solution yr yr yr yr yr yr
Case Study E: Diffusive Mixing 2 myr 20 myr 80 myr 400 myr 0 0.5 1
Case Study F: n-component
Case Study G: Rayleigh Number
Case Study H: Reservoir with Baffle for n-component Mixing Kx = 100 md in reservoir Kx = 10, 1, 0.1, 0.0001 md in baffle nc4 mole fraction Kz = 10 md in reservoir Kz = 1/10 of Kx in baffle C1 mole fraction Pressure gradient (atm)
Case Study H: Reservoir with Baffle for n-component Mixing (cont d)
Case Study I: Effect of Pressure and Thermal Diffusions Equilibrium at t = 17 million years with pressure diffusion Equilibrium at t = 20 million years with thermal diffusion Equilibrium at t = 19 million years with pressure and thermal diffusions
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.