Comparison between Darcy and Invasion Percolation Simulations of Kilometer Scale Hydrocarbon Migration across Fine Grained Sediments: An Example from the Malvinas Basin, Offshore Argentina

Andre Vayssaire
YPF, Buenos Aires, Argentina

Geological framework
The Malvinas basin (Figure 1) formed in response to early rifting and volcanism related to the first break-up of the Gondwana. It was followed by a quiet phase of post-rift thermal subsidence throughout the Cretaceous which led to a marine transgression and developed back stepping sands (Springhill Formation). The transpressional deformation acting along the South America-Scotia plate boundary deepened the southern part of the basin. This led to a fold and thrust belt developed essentially during Oligocene and Lower Miocene forming the southernmost limit of the Malvinas foreland basin.

Today exploration focuses in the South of the basin. Targeted reservoirs are of Miocene to Eocene ages, a few thousands meters above the Lower Cretaceous source rock. Faults cannot be evoked as conduits for the hydrocarbons and only kilometer scale vertical displacement could explain reservoir infilling.

Hydrocarbon migration across fine-grained sediments
Displacement of the hydrocarbons through significant thicknesses of fine grained rocks is becoming a migration process more and more accepted by the industry. Aplin and Larter (2005) consider that most of the world petroleum has migrated vertically through large thicknesses of fine-grained sediments. But estimating the flow rates is extremely difficult since it is such a slow process at our time scale that laboratory experiments are very challenging. Whereas oil can flow at a few centimeters per hour in reservoir rocks, Appold and Nunn (2002) predicted oil migration in fine-grained sediments on the order of 100 m/Ma (0.1mm/year) which still allows a one kilometer vertical migration in 10 Ma. Neuzil (1994) and Dewhurst et al. (1999) calculated a hydraulic conductivity between 0.01mm to 1km per Ma.

Migration simulations in the Malvinas basin
In the Malvinas basin, the Darcy simulator from IFP (Rueil Malmaison, France) and the Invasion Percolation simulator from Permedia Research Group’s (Ottawa, Canada) were used to model in the three dimensions hydrocarbon migration. The IFP model assumes that the hydrocarbons migrate as a separate phase and follow the Darcy’s laws which give a complete description of the fluid flow taking into account the intrinsec permeability tensor, the relative permeabilities in the porous medium, the viscosity, the density, the capillary pressure of the hydrocarbon phase and the pore pressure of the water phase (Ungerer et al., 1984). The Invasion Percolation (IP) technique considers that the balance between the buoyancy and the capillary forces overwhelmingly controls the trajectories of the hydrocarbon flow (Carruthers, 2003) and that the migration distance and velocity is predominantly controlled by the volume of petroleum expelled from the source rock.

Both simulations show great similarities in the present day saturation distribution of the Miocene and Eocene layers (Figure 2), nevertheless, the charging process of the two models is very different. With Darcy, the oil that fills the reservoir comes from the top of the oil migration front whereas with the IP technique, the early expelled oil has already migrated through the entire system up to the surface and the oil filling the reservoir was recently expelled. This result seems to be more in accordance with sea bottom piston coring results and other DHIs suggesting that the hydrocarbons have reached the seafloor in great quantities.

In other words, although in both cases we have saturation within the Miocene reservoirs with IP most of the hydrocarbons out flooded the sea floor surface whereas with Darcy, most of the petroleum sits in low permeable layers between the source rock and the reservoirs. In reality, these huge quantities of hydrocarbon within low permeability rocks, often seen in Darcy simulation results, are unlikely to be there since evidences of active secondary migration pathways are rarely reported.

Migration losses
Sylta (2002) and other authors mentioned that Darcy may overestimate the hydrocarbon losses and that calculated migration velocities are too low. In fact, it looks as if the losses control the migration velocity. Decreasing the migration losses by increasing the residual water saturation does not change the velocity calculated by the Darcy equation but forces the migration to move faster and further since the petroleum saturation reaches more rapidly the maximum saturation threshold value and the extra mass is then forced to move where the hydraulic head is the lowest (usually upward) whatever the Darcy solver says. The same occurs when increasing the expelled masses of the source rock, no change in the velocity calculated by Darcy but the hydrocarbons move along a greater distance (Figure 3).

Relative permeabilities of fine grained sediments are poorly controlled due to the difficulty of doing measurements on low permeability rocks. Okui and Waples (1993) extrapolated relative permeabilities measured in rocks with decreasing grain size from sand to silt and showed that the residual water saturation in shales increases significantly reducing the maximum hydrocarbon saturation to approximately 20% in low permeability rocks. The same authors also showed that the flow of oil commences in fine grained rocks at increasingly small oil saturation (i.e. 2%).

Furthermore, whereas migration within a reservoir has a piston like displacement pattern, several authors like Luo et al., (2007), Carruthers (2003), Schowalter (1979), and Berg (1975) consider that oil migrates along thin stringers in fine grained sediments. We can then consider that migration pathways cover an area that is hundred or even thousands times smaller than the cell area used for the simulation. This decreases considerably the cell maximum hydrocarbon saturation. Assuming that within the migration pathway the maximum oil saturation is 20% at the scale of the simulation cell this number drops down to values lower than 0.2% and under these conditions, what governs the migration is not the parameters of the Darcy equation but the amount of petroleum in the system (source rock expulsion) and the stratigraphic architecture (buoyancy and capillary forces).

Conclusion
The simplification of the Darcy law considering instantaneous migration gives the equation that controls the hydrocarbon migration by percolation (Schneider 2003). Carruthers (2003) considers that this simplification is appropriated and that viscous forces can be ignored based on the work of England (1987) that showed that at geological flow rate of secondary migration, the capillary number never exceeds 1e-10 which is far below the 1e-4 limit from which viscous forces become important.

It was just shown that when using appropriate relative permeability curves, the petroleum migration distance and velocity are overwhelmingly controlled by the expulsion of the hydrocarbons from the source rock (timing, quantities and products) and that the viscosity and permeability forces can be neglected.

References
Aplin A. C., and S. R. Larter, 2005, Fluid flow, pore pressure, wettability, and leakage in mudstone cap rocks, in P. Boult and J. Kaldi, eds., Evaluating fault and cap rock seals: AAPG Hedberg Series, no. 2, p 1-12.

Appold M. S., and J. A. Nunn, 2002, Numerical models of petroleum migration via buoyancy-driven porosity waves in viscously deformable sediments, Geofluids, Vol. 2, p. 233-247.

Berg R. R., 1975, Capillary pressures in stratigraphic traps: AAPG Bulletin, v. 59, p. 939-956.

Carruthers D.J., 2003, Modeling of secondary petroleum migration using invasion percolation techniques, in S. Duppenbecker and R. Marzi, eds., Multidimensional basin modeling, AAPG/Datapages Discovery Series No. 7, pp. 21-37.

Dewhurst D. N., Y. L. Yang, and A. C. Aplin, 1999, Permeability and fluid flow in natural mudstones, in A. C. Aplin, A. J. Fleet and J. H. S. Macquaker, eds., Muds and mudstones: Physical and fluid-flow properties: Geological Society (London) Special Publication 158, p. 22-43.

England W. A., A. S. Mackenzie, D. M. Mann, and T. M. Quigley, 1987, The movement and entrapment of petroleum fluids in the subsurface: Journal of Geological Society of London, v. 144, p. 327-347.

Luo X. R., B. Zhou, S. X. Zhao, F. Q. Zhang and G. Vasseur, 2007, Quantitative estimates of oil losses during migration, Part I: the saturation of pathways in carrier beds, Journal of Petroleum Geology, Vol. 30(4). October 2007, p. 375-387.

Neuzil C. E., 1994, How permeable are clays and shales? Water Resources Research, v. 30, p. 145-150.

Nunn J.A., P. Meulbroek (2002) Kilometer-scale upward migration of hydrocarbons in geopressured sediments by buoyancy-driven propagation of methane-filled fractures. AAPG Bulletin, v. 86, No. 5, pp 907-918.

Okui A, and D. W. Waples, 1993, Relative permeabilities and hydrocarbon expulsion from source rocks, in A. G. Dore et al., eds., Basin Modelling: Advances and Applications: Amsterdam, Elsevier, p. 293-302.

Schneider F., 2003, Modeling multiphase flow of petroleum at the sedimentary basin scale, Journal of Geochemical Exploration 78-79, p. 693-696.

Schowalter T. T., 1979, Mechanics of secondary hydrocarbon migration and entrapment. AAPG Bulletin, v. 63, p. 723-760.

Sylta O., 2002, Quantifying secondary migration efficiencies. Geofluids, Vol. 2, pp. 285-298.

Ungerer P., F. Bessis, P.Y. Chenet, B. Durand, E. Nogaret, A. Chiarelli, J.L. Oudin, and J.F. Perrin, 1984, Geological and geochemical models in oil exploration: principles and practical examples. Petroleum Geochemistry and Basin Evaluation, AAPG, Geol. Mem. No. 35, 53-77.

Figure 1. Malvinas basin localisation and stratigraphic column.