Simulation of Petroleum Migration inFine-Grained Rock by Upscaling RelativePermeability Curves: The Malvinas Basin,Offshore Argentina

Andre Vayssaire

Repsol Exploration, Madrid, Spain

ABSTRACT

Early exploration of the Malvinas Basin (1979–1991) targeted Lower Cretaceous

sandstones assuming that hydrocarbons would migrate laterally from the basin

depocenter in the south to structures located in shallow water. Hydrocarbons

were found, but not in large enough quantities to be commercially viable. Recently,

exploration has moved closer to the depocenter and focuses on Eocene to Miocene

sandstones a few thousandmeters vertically above themature Lower Cretaceous source

rock. As no faults crosscut the entire section between the source rock and reservoirs, they

cannot be evoked as conduits for hydrocarbon migration. Therefore, kilometer-scale

vertical migration across fine-grained sediments was considered as the main process to

transport hydrocarbons from source rock to reservoir.

This migrationmechanism is commonlymentioned, but poorly constrained. Darcy

flow and invasionpercolation calculatorswere used to simulate hydrocarbonmigration.

If we consider that hydrocarbons migrate along thin stringers, the relative permeability

parameters have to be upscaled to consider that not all of the rock is being saturated by

petroleum. Furthermore, fine-grained sediments present a very high specific area,which

gives a higher sorption capacity for water, and therefore, less petroleum is needed to

reach the saturation threshold for flow. Secondary migration across fine-grained sedi-

ments takes time to initiate, but as soon as hydrocarbons invade the pore space, the

migration is effective; it occurs with minimal hydrocarbon losses and is essentially

controlled by the expulsion rate of petroleum from the source rock and the stratigraphic

architecture. From a physics standpoint, the Darcy method looks more appropriate be-

cause it incorporates the full physics of the problem. However, under these conditions,

viscous forces can be ignored and the invasion percolationmethod seems appropriate to

simulate secondary migration of hydrocarbons across fine-grained sediments.

15Vayssaire, A., 2012, Simulation of petroleum migration in fine-grained rock by

upscaling relative permeability curves: The Malvinas Basin, offshore Argentina,in K. E. Peters, D. J. Curry, and M. Kacewicz, eds., Basin Modeling: New Horizonsin Research and Applications: AAPG Hedberg Series, no. 4, p. 247–257.

247

Copyright n2012 by The American Association of Petroleum Geologists.

DOI:10.1306/13311440H43474

GEOLOGIC FRAMEWORK

The Malvinas Basin (Figure 1) is the southernmost

offshore sedimentary basin in Argentina with water

depths ranging from 50 to 1000m (164–3281 ft). It has

a triangular shape (Figure 2) and is limited by the Rio

Chico High in the west, onlaps onto the Malvinas plat-

form to the east, and is constrained to the south by theBurwoodBank,which is a topographic expressionof the

fold and thrust belt associated with the South America

andScotia plates. TheMalvinas Basin formed in response

to early rifting and volcanism related to the first breakup

of Gondwana (Vayssaire et al., 2008), which caused the

separation of eastern Gondwana (India, Australia, and

Antarctica) fromwesternGondwana (SouthAmerica and

Africa) in the Late Jurassic (168 Ma). In the MalvinasBasin, the termination of this synrift period correlates

withoceanic crust formation in theWeddle Sea (150Ma).

It was followedby a phase of postrift thermal subsidence

throughout the Cretaceous that led to a marine trans-

gression and developed the backstepping sands of the

Springhill Formation (Figure 3). The transpressional de-

formation acting along the South America–Scotia plate

boundary deepened the southern part of the basin. Thisled to the development of a fold and thrust belt during

theOligocene and the lowerMiocene, forming the south-

ernmost limit of the Malvinas foreland basin.

The Springhill Formation was targeted during the

early exploration of the basin (1979–1991). This explo-

ration has proven the existence of a working petroleum

system, albeit without the discovery of commercially

viable petroleum accumulations. This economic failureis most likely caused by poor efficiency of lateral mi-

gration of the hydrocarbons from the depocenter to-

ward the structures.

Today, exploration focuses in the southern part of

the basin. Targeted reservoirs are of Eocene to Miocene

age, a few thousandmeters above the Lower Cretaceous

source rock. Only kilometer-scale vertical migration of

hydrocarbons can explain reservoir infilling.

HYDROCARBON MIGRATIONACROSS FINE-GRAINED

SEDIMENTS

Aplin and Larter (2005) believe that most of theworld’s petroleum migrated vertically through large

thicknesses of fine-grained sediments. Estimating the

flow rates is extremely difficult because it is such a slow

process that laboratory experiments are very challeng-

ing and, in most cases, impossible.

Whereas oil can flow at a few centimeters per hour

in reservoir rocks, Appold and Nunn (2002) predicted

oilmigration in fine-grained sediments is in the order of

100 m/Ma. This still allows 1 km (0.6 mi) of vertical mi-

gration in 10Ma, but represents only 0.1mm/yr. Neuzil

(1994) andDewhurst et al. (1999) calculated a hydraulic

conductivity between 0.01 mm/m.y. and 1 km/m.y.

The mechanism of hydrocarbon secondary migra-

tion across fine-grained sediments is alsonotwell under-

stood. For primary migration, Appold and Nunn (2002)

ventured thehypothesis of the porositywave thatwouldfavor the displacement of hydrocarbons within the

source rock. Osborne and Swarbrick (1997) showed that

the release of hydrocarbons from kerogen during crack-

ing would lead to an increase of fluid volume and pore

pressure, generatingmicrofractures and primarymigra-

tion of hydrocarbons in low-permeability source rocks.

This hypothesis is supported by observations that the

top of the overpressure section commonly coincideswith the petroleum generation window (Spencer, 1987;

Isaksen 2004).

Regarding the formation of hydrocarbon pathways

during secondary migration, Aplin and Larter (2005)

demonstrated that polar compounds inpetroleum, such

as phenols, penetrate the mineral water films such that

hydrocarbons can wet the mineral surface. In this case,

cap rocks do not act as permanent seals, but simply re-tard the inexorable flow of petroleum. Other migration

mechanisms have been proposed, including migration

because of fracturing of the cap rock when the buoy-

ancy forces exceed the tensile strength of the rock or the

propagation of methane-filled fractures that develop

the potential to entrain and transport oil (Nunn and

Meulbroek, 2002).

It appears that the processes previously mentionedtake time to initiate, but as soon as hydrocarbons in-

vade low-permeability rock, more petroleum can mi-

grate through this pathway very easily and rapidly even

in the absence of a pressure gradient to driveDarcy flow.

Existing pathways can be reused in a very efficient way

with a quasi-instantaneous velocity andminimal hydro-

carbon losses.

MIGRATION SIMULATIONS INTHE MALVINAS BASIN

In the Malvinas Basin, the Temis Darcy simulator

from IFP (Institut Francais du Petrole, RueilMalmaison,

France) and the MPath invasion percolation (IP) simu-lator from The Permedia ResearchGroup (Ottawa, Can-

ada)wereused tomodel hydrocarbonmigration in three

dimensions. The IFP model assumes that the hydrocar-

bonsmigrate as a separatephase and followageneralized

Darcy’s law (Bear, 1972),whichgives a complete descrip-

tion of the forces controlling the fluid flow considering

the intrinsic permeability tensor, the relative perme-

abilities in the porous medium, as well as the viscosity,

248 Vayssaire

density, and capillary pressure of the hydrocarbonphase

and the pore pressure of the water phase (Ungerer et al.,

1984). The IP technique considers that the balance be-tween the buoyancy and the capillary forces overwhelm-

ingly controls the trajectories of the hydrocarbon flow

and that the migration distance and velocity is predom-

inantly controlled by the rate and volume of petroleum

expelled from the source rock (Carruthers, 2003), and

hence, the viscous forces are ignored.

Both simulations show great similarities in the

present-day saturation distribution in the Miocene andEocene reservoirs (Figure 4). Bothmodels have the same

lithologic descriptionand contain realistic stratigraphic

variability. The calculated temperatures andpressures are

identical at all ages. The rock parameters such as poros-

ity, capillary pressure, and relative permeability curves

are also identical. The grid resolution is vertically the

same, but the Darcy model was laterally upscaled to de-

crease the number of grid cells to reduce the calculationtime. This upscaling has no effect on the migration

mechanism and the distribution of the hydrocarbon

accumulations.

Nevertheless, the charging process of the twomod-

els is very different. With Darcy flow, the oil that fills

the reservoir comes from the top of themigration front,

whereaswith the IP technique, the early expelledoil has

already migrated through the entire column up to thesurface, and theoil filling the reservoir has been recently

expelled. This result seems to be more in accordance

with sea bottom piston-coring results and other direct

hydrocarbon indicators, suggesting that the hydrocar-

bons reached the sea floor in great quantities.

FIGURE 1. Map of Argentinawith the principal sedimen-tary basins.

Simulation of Petroleum Migration in Fine-Grained Rock 249

In otherwords, with IP,most of the expelled hydro-

carbons reach the sea floor, whereas with Darcy flow,

most of the petroleum remains in low-permeability lay-

ers between the source rock and the reservoirs. Figure 5displayshydrocarbonsaturationduring theMiocenealong

a cross section extracted from two three-dimensional

blocks resulting fromDarcy and IP simulations. The satu-

rations in the Darcy simulation are high between the

source rock and ‘‘Sand-1.’’ The IP simulation showsmuch

lower saturations andmigration pathways up to the sur-

face. Abundant hydrocarbons leave the model bound-

ary through the sea floor, which is not the case with theDarcy simulation.

The interpretation for the migration risk is very dif-

ferent. In the Darcy case, the risk is that the expulsion

occurs too late and the hydrocarbons have no time to

reach the target. In the IP case, the source may mature

too early and the expelled hydrocarbonmigrates to the

sea floor, leaving an insufficient charge to fill the reser-

voirs once the trap is formed and sealed.With the IPmethod, in fine-grained sedimentswhere

no contrast of capillary pressure exists, thehydrocarbon

flows fromone grid cell to another as soon as the critical

saturation is reached.With Darcy, the calculated veloc-

ity is generally too slow to permit flow and the satura-

tion continues to increase until petroleum occupies the

maximum possible volume. At this stage, all mobile

water has flooded out of the pore space. An additional

increase of saturation will force the petroleum to moveout of the grid cell so the saturation does not exceed the

maximum value permitted. This displacement is there-

fore essentially controlled by the saturation limits of the

relative permeability curves, and viscous forces play a

nominal role.

Beyond the Malvinas case, these two different re-

sults confirm that the quantity of petroleum found in

the reservoirs represents a small fraction of what wasgenerated. McDowell (1975) and Moshier and Waples

(1985) concluded that the recoverable quantity of pe-

troleum inmost basins is only a few percent of the gen-

erated petroleum, and in very few cases does this num-

ber reach 10%. This demonstrates the inefficiency of

one or all of the following poorly understood processes:

expulsion, migration, and trapping of hydrocarbons.

Pepper andCorvi (1995) consider thathydrocarbons aresorbedwithin the kerogen (adsorbed in themicroporos-

ity and absorbedonto the internal surface area) and that

the cracking of 200 mgHC/gC of initial hydrogen index

(HI) is a prerequisite for oil expulsion. It is also generally

accepted that cap rocks do not act as permanent seals

FIGURE 2. Geologic framework of the Malvinas Basin and the surroundings. DSDP = Deep Sea Drilling Project.

250 Vayssaire

but retard the flow of petroleum and that reservoir col-

umn heights are essentially controlled by the balancebetween buoyancy and capillary forces. During migra-

tion, hydrocarbons are lost along the migration path-

ways because of the heterogeneity of the stratigraphic

architecture but also because the rockmust reach amini-

mum petroleum saturation before oil can flow. These

losses are a challenge to quantify.

MIGRATION LOSSES

Sylta (2002) and other authors mention that simu-

lators using modified Darcy equations may overesti-

mate hydrocarbon losses, and therefore, the calculated

migration velocities are too low. The simulation of hy-

drocarbon migration in low-permeability rock using

Darcy’s law (Figure 6) clearly shows that the calculatedDarcy true velocities never exceed 3.6 m/m.y., and the

average velocity is around 0.5 m/m.y. These numbers

cannot explain the present-day migration front 2.5 km

(1.5 mi) above the top of the source rock, with the ex-

pulsion starting at 120 Ma. The migration rate must ex-

ceed 20m/m.y. to account for the migration front loca-tion at present day.

In fact, it looks as if the losses have a significant

impact onmigration velocity. Under certain conditions,

decreasing migration losses by increasing the residual

water saturation does not significantly affect the veloc-

ity calculated by the Darcy equation but forces the mi-

gration tomove faster and furtherbecause thepetroleum

saturation rapidly approaches themaximum saturationthreshold value. The extra mass is then forced to move

where the hydraulic head is the lowest (commonly up-

ward) whatever the velocity calculated by the Darcy

solver. Two synthetic cross sections are shownat the top

of Figure 7. The only difference between the two sec-

tions is the maximum hydrocarbon saturation allowed

in each grid cell. On the left, the relative permeability

curve allowsmaximumhydrocarbon saturation to reach100%. Themean true Darcy flow calculated is 4m/m.y.,

and the migration front at present day is around 1 km

(0.6mi) above the top of the source rock (bottom layer).

At the right, themaximumhydrocarbon saturationwas

FIGURE 3. Stratigraphic column of the Malvinas Basin with petroleum system elements and major tectonic imprints.

Simulation of Petroleum Migration in Fine-Grained Rock 251

reduced to 30%. Themigration velocity did not change

much (5m/m.y. instead of 4m/m.y.), but themigration

frontmovedmuch farther (4000m [13,123 ft] insteadof

1000 m [3281 ft]).

The sameoccurswhen increasing theexpelledmasses

from the source rock: no change in the velocity calcu-

lated by theDarcy technique is observed, but the hydro-

carbons move a greater distance (Figure 7, bottom).

FIGURE 5. Simulation results from invasion percolation (IP) (right) and Darcy (left) simulators showing hydrocarbonsaturation during the Miocene.

FIGURE 4. Simulation results showing hydrocarbon distribution (saturation) in Miocene reservoirs using the invasionpercolation method (right) and Darcy’s law (left).

252 Vayssaire

The relative permeabilities of fine-grained sedi-

ments are poorly controlled because of 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 in-

creasingly small oil saturations (i.e., 2%). The expla-

nation given is that the clays in rock provide enormous

specific area, giving a higher sorption capacity for wa-

ter. This increases the film of immobile water surround-

ing the grains. This film is commonly referred to as

‘‘bound’’ or ‘‘connate water.’’ The consequence is that

compared with sandstones, low-permeability rocks re-

quire less petroleum to reach the saturation thresholdfor migration to occur, which leads to lower migration

losses.

FIGURE 6. Top: Synthetic cross section showing present-day hydrocarbon saturations. The source rock is located inthe bottom layer, and the migration front is more than 2500 m (8202 ft) above it. Bottom: Hydrocarbon migrationvelocity in meters per m.y. for each cell versus geologic time in m.y. The red line at the left represents the history ofhydrocarbon migration true velocity of the cells just above the source rock. The green line gives the velocities ofthe second row of cells above the source rock, and so on.

Simulation of Petroleum Migration in Fine-Grained Rock 253

UPSCALING RELATIVEPERMEABILITY CURVES

Whereas migration within a reservoir may have a

pistonlike displacement pattern, where the saturation

at the migrating cluster is high, several authors includ-

ing Luo et al., (2004, 2007, 2008), Carruthers (2003),

Meakin et al., 2000, Schowalter (1979), and Berg (1975)

consider that oil migrates along thin stringers in fine-

grained sediments where the saturation is low. As dem-

onstrated by Luo et al., 2007, themigration starts with-in the source rock with many columns of petroleum

moving upward. Gradually, some columns stop, one

after the other, and only a few migration pathways

continue to grow. After the saturation has built up

within the narrow continuous pathways that have de-

veloped, the migration process is considerably faster

and oil tends to migrate efficiently within a limited

number of pathways. The result is that the migrationlosses are much higher within and close to the source

rock than outside and far from the source rock, where

they may be negligible. This is in accordance with the

very few reports of active migration pathways and the

important quantities of petroleum that can be found

in source rocks (e.g., shale-gas). Luo et al. (2007) con-

sider that about 99%of the losses occurwithin the range

of the source area, andHirsh and Thompson (1995) dem-

onstrated that the remaining saturations in secondary

migration can be in the order of 1%.

The rock samples used in the experiments aremuch

smaller than the grid blocks used inbasinmodels.Withinthe rock volume represented by these grid blocks, a large

fraction would never be exposed to petroleum. The crit-

ical saturations used by the simulators should therefore

be scaled by a function of the grid cell area, assuming

thatmigration is essentially vertical in low-permeability

rocks. To account for the large number of stringers, the

scaling might be turned off inside and near the source

rock. It should then increase as petroleum moves awayfrom the source rock.

We should then consider that migration pathways

outside the source rockcover anarea that ismuch smaller

than the cell area used for the numerical simulation.

When petroleum saturates a migration pathway to its

critical saturation, it does not impact the entire simula-

tion cell but instead a small volume corresponding to

the stringers. The maximum hydrocarbon saturationwithin a migration pathway needs to be upscaled to re-

flect the mean value inside the entire numerical simu-

lation cell. Assuming thatwithin themigrationpathway

the maximum oil saturation is 20% at the scale of the

simulation cell, this number may drop to values lower

than 0.2%. Thiswould correspond to a 1-km2 (0.39mi2)

simulation cell in which we assume that the migration

stringers occupy an area of 100 m2 (1076 ft2).

FIGURE 7. Hydrocarbon (HC) saturation in two identical synthetic sections with different maximum HC saturation(top) and total organic carbon (TOC) (bottom).

254 Vayssaire

DISCUSSION

Schneider (2003) (Figure8, right) claims that succes-sive simplifications of Darcy’s law that neglect excess

pressure, assuming that fluids are not compressible and

considering thatmigration is instantaneouswith respect

to geologic time, result in an equation governing the

models that is controlled by percolation (Carruthers and

de Lind van Wijngaarden, 2000).

Whereas the generalized Darcy equation contains

threedriving forces forhydrocarbonmigration,whicharebuoyancy, capillary forces, andviscous forces,Carruthers

(2003) considers that viscous forces can be ignored.

Englandet al. (1987) showed that at thegeologic flowrate

of secondary migration, the capillary number (Figure 8,

left) never exceeds 1e-10,which is far below the1e-4 limit

at which viscous forces become important.

The Darcy method has proved its efficiency for res-

ervoir production simulation.UsingDarcy-basedmigra-tion solvers to representmigration at basin scale assumes

that all of the physics appropriate for reservoir simulation

must extend to basin time and length scales, although

we know significant differences exist with the require-

ments of the two scenarios (grain size, saturation, grid

cell, permeability, and particularly, time).

Experience shows that velocities, calculated using

the Darcy equation, are too small to explain migration

in low-permeability mudstones. Furthermore, numeri-

cal difficulties andhigh run times are encounteredwhen

runningDarcywith upscaled relative permeability curvesthat can discourage the use of high-resolution models,

and therefore reduce their use as predictive tools.

Figure 9 shows a sensitivity analysis of maximum

hydrocarbonsaturation insecondarymigration simulation

cells. It clearly demonstrates that with high values (be-

tween10and15%), fewhydrocarbons reach the reservoir

and none flow to the surface. The risk is that the ex-

pulsion occurs too early. At 5% saturation, 23% of theexpelled hydrocarbons migrated to the surface and the

reservoirs received themaximumquantity of petroleum.

With values lower than 4%,more hydrocarbons are lost

in the sea floor and the volume in reservoir does not

vary much.

Of course, great uncertainty is present with respect

to the selected upscaled value, but it appears, as shown

in this representative example, that as long as it has thecorrect order ofmagnitude, it does not greatly affect the

simulation results.

CONCLUSIONS

The calculationsof hydrocarbonmigrationdetailed

here were achieved using the Darcy simulator from IFP

FIGURE 8. Arguments from Carruthers (2003) to justify that viscous force can be ignored (left) and demonstration fromSchneider (2003) that invasion percolation can be derived from Darcy’s law (right).

Simulation of Petroleum Migration in Fine-Grained Rock 255

and the IP calculator from Permedia. Although they

show similar present-day saturations inside the poten-tial reservoirs, the saturation distribution outside the

reservoir is drastically different because of differences in

migration history. With Darcy flow, most of the petro-

leum remains between the source and the reservoir in

low-permeability rocks. With IP, most of the hydrocar-

bons flowed through the topographic surface. The latter

result seems to be more in accordance with sea bottom

piston-coring results and other direct hydrocarbon in-dicators, suggesting that the hydrocarbons reached the

sea floor in great quantities.

Furthermore, all simulationsusingDarcy’s law show

relatively high saturations in low-permeability rocks be-

hind the migration front, which has a pistonlike dis-

placement pattern. This is something that is not con-

firmed by drilling, which reports very rare evidence of

active secondary migration paths.Fromaphysics standpoint, theDarcymethod looks

more appropriate, as it incorporates the full physics of

the problem.However, upscaling the relative permeabil-

ity curves is necessary tomimic amigration process that

is supposed to occur along thin stringers. Under these

conditions, the Darcy velocities do not change much,

whereas the migration front moves further and numer-

ical difficulties increase. It appears that viscous and per-meability terms can be ignored for calculating displace-

ment of hydrocarbons across fine-grained sediments,

and the IP technique provides satisfactory and realistic

results. The petroleum migration distance and velocity

are overwhelmingly controlled by the hydrocarbon ex-

pulsion rate from the source rock (timing, quantities,

andproducts) and the stratigraphic architecture (anisot-

ropy, buoyancy, and capillary forces).

Manyunknowns remain inmigration and expulsion

processes. These unknowns have strong consequencesin our simulations of reservoir filling. The oil and gas

found in reservoirs represents a small fraction of what

has been generated, which raises questions about the

fate of the unaccountedmass. This emphasizes theneed

formore research intowhat happens in the source rock,

not only the generation, but also the expulsionphenom-

ena (retention, primary migration, expelled quantities,

products, and the timing) and the secondary migrationprocesses.

ACKNOWLEDGMENTS

I thank the management of YPF Exploration for

support andpermission topublish,WicaksonoPrayitno

for the long conversations we had about petroleumsystems in the South Atlantic, and Frederic Schneider

andDanCarruthers for interesting discussions about oil

and gas secondary migration. Appreciation is also ex-

pressed for David Kennedy, Kenneth Peters, and an

anonymous reviewer for helpful technical and editorial

comments.

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