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WHY LIGHT HYDROCARBONS DO NOT FORM A GAS PHASE AFTER DIFFUSING THROUGH SEALS
Alton Brown
Richardson, Texas
([email protected])
Search and Discovery #40017 (2001)
This article is presented along with article entitled “Geochemical Characterization of Natural Gas: A Physical Multivariable Approach and Its Applications in Maturity and Migration Estimates” by Alain Prinzhofer et al. (Search and Discovery #40016; AAPG Bulletin, 2000, v. 84, p. 1152-1172) as a forum for discussion of hydrocarbon migration.
Three processes limit the
formation of a mobile gas after diffusion in and through a seal
. First, gas
dissolved in
seal
pore water is insufficiently supersaturated to form a mobile
gas due to capillary effects, so diffusive path length must be at least as great
as the
seal
thickness. Second, diffusivity is generally higher in coarse-grained
rocks than in seals, so diffusive losses from the interval above the
seal
are
likely to equal diffusive supply through the
seal
as partial pressures
approaches saturation. If so, no
gas forms. Third, compositional fractionation between reservoired and exsolved
gases reduces the methane overpressure necessary for gas exsolution above the
seal
.
Unless confining pressure
decreases, exsolution of large quantities of gas after diffusion only occurs
under the rare circumstances of exceptionally tall gas columns (thousands of
meters) and thin shale seals (<10 m). I
am not aware of any field with the combination of features necessary to exsolve
a gas above the seal
. No mechanism yet proposed can cause exsolution of large
quantities of gas after diffusion without major changes in confining pressure
and temperature. For this reason, I
find it difficult to interpret gas geochemical trends from conventional gas
accumulations in continuously subsiding basins as products of diffusion
modification during migration.
Figure 1. Methane
partial pressure in seals at steady diffusion.
A. Homogeneous
seal
. Maximum
capillary pressure occurs at the base of the
seal
and decreases up section.
B. Two layer heterogeneous
seal
, where the lower
seal
layer has lower diffusivity. Pm
is lower than the single layer case. C.
Two layer heterogeneous
seal
, where the lower layer has higher diffusivity. Pm
is higher than the single layer case, and may exceed Pd
of the lower layer. D. As the
number of alternating higher and lower diffusivity layers increase, deviations
from the average Pm trend are less, so it is less likely for Pm
to exceed the capillary displacement pressure.
Figure 2. Concentration
(as partial pressure) vs. depth for steady diffusion of methane through a
seal
where a gas phase forms above the
seal
. Methane
concentration gradient in the
seal
is controlled by the pressure in the
underlying gas reservoir, the requirement to form a gas phase above the
seal
,
and the thickness of the
seal
. The minimum possible methane partial pressure
gradient in the overlying sandstone is the hydrostatic gradient G if water is
gas-saturated at the
seal
-sandstone interface.
Figure 3. Possible relationships between reservoir
gas pressure and hydrostatic pressure above the
seal
where the gas must exsolve.
(1) If the reservoir gas pressure is less than the hydrostatic pressure above
the
seal
, diffusion upwards through the
seal
is impossible.
(2) If reservoir pressure is higher than the hydrostatic pressure at the
top of the
seal
, but the overpressure is negative formation of a gas phase
requires that diffusivity of the
seal
exceed that of the rock over the
seal
,
which is inconsistent with experimental data and theory.
(3) If the overpressure is positive, then formation of a gas phase is
possible where the ratio of the
seal
to sandstone diffusivity is less than the
ratio of the
seal
to sandstone concentration gradients.
Figure 4. Calculated
relative diffusivity necessary to form a gas phase above a
seal
with and without
gas compositional effects. Under the conditions assumed here, a gas column of at
least 415.3 m is required for Dsh/Dss <1 where
compositional differences affect diffusion. Assumed conditions are hydrostatic
pressure gradient, reservoir depth of 3 km, gas density of 0.15 g/cc, and
methane fraction of 0.85 in the reservoir gas and 0.95 in the gas exsolved above
the
seal
. Gas columns of 10, 100,
and 1000 m create capillary pressures of 0.085, 0.85, and 8.5 MPa, respectively.
Figure 5. Methane
partial pressures (blue circles) where exsolved gas is drier than the reservoir
gas. The difference in methane
partial pressure is less than the difference in total pressure (red circles).
The methane partial pressure of a wet gas in the reservoir may be less than that
of exsolved gas above the
seal
. In
this example, the total gas overpressure (P) is positive, but the methane gas
overpressure (P*) is negative.
Reasons Why Gas Does Not Form Above the Seal
Gas Formation
in the Seal
Effects of Compositional Variation
Gas diffusion through seals has
been proposed to explain two phenomena: isotopically depleted, dry gases in
conventional gas accumulations, and shortened life of gas accumulations. Some
geochemists (e.g., Prinzhofer et al. 2000) believe that many isotopically
depleted, dry gases are results of diffusive fractionation through seals.
Kinetically fractionated gases can form conventional accumulations only where
gas forms and migrates, so formation of a gas within and above the seal
is
essential. If gas remains in solution after diffusion, then it cannot migrate to
shallower accumulations.
The purpose of this document is
to show why formation of a gas from hydrocarbons which have diffused through a
seal
is unlikely or impossible in most geological settings.
We will look at two issues, the diffusion process and the process of formation of a gas from dissolved light hydrocarbons.
The diffusive flux is proportional to the effective diffusivity and to the negative of the concentration gradient of the diffusing species (Fick's first law; e. g. Welty et al., 1969). During one dimensional, vertical diffusion of a hydrocarbon dissolved in pore water, the hydrocarbon accumulates if the vertical diffusive flux decreases upwards in the zone (as described by Fick's second law; Welty et al., 1969). Effective diffusivities are fixed for a given problem, but concentration gradients change with time as dissolved gases diffuse. If the range of concentration gradients corresponding to different effective diffusivities can be identified, then conditions where dissolved methane can accumulate sufficiently to form a gas phase can be identified.
Concentration of the diffusing
hydrocarbons will be expressed as partial pressure, the mole fraction of a gas
phase multiplied by the total gas pressure (Welty et al. 1969). This can be done
because light hydrocarbon concentration in water is proportional to its fugacity
as described by Henry's law (Garrels and Christ 1965). Ideal gas behavior will
be assumed, so fugacity is approximated by partial pressure. At the temperatures
and pressures of interest, gas does not behave ideally.
However, pressure and temperature change over the thickness of the seal
are not likely to be significant, so deviations from ideal behavior will be
approximately the same at all points on the diffusion pathway.
Ideal gas behavior is assumed, so a gas forms where the sum of the partial pressures equals the fluid pressure in the absence of capillary effects (Dalton's Law; Welty et al. 1969). The term "gas" refers to a phase, not a composition. "Methane" or "light hydrocarbon" refers to chemical species. Unless compositional effects are addressed, methane is assumed to be the only dissolved hydrocarbon species, so a gas phase will form where the methane partial pressure equals the total pressure in the absence of capillary effects. Likewise, methane gas will not be present if the methane partial pressure is less than the total pressure.
The pressure difference between
gas and water in a reservoir is the capillary pressure. The hydrocarbon
capillary pressure is the difference between the partial pressure of the
hydrocarbon and the pressure required to form a gas phase under conditions of
interest. Undersaturated water
therefore has a negative hydrocarbon capillary pressure.
The term "capillary displacement pressure" is the capillary
pressure necessary to form a gas which can migrate through the pore system.
Where the hydrocarbon capillary pressure is less than the capillary displacement
pressure, any exsolved gas is immobile, so the rock acts as a seal
.
REASONS WHY GAS DOES NOT FORM ABOVE THE SEAL
There are three reasons why
exsolution of gas diffused through a seal
is unlikely in most geological
settings. (1) A mobile gas cannot form in an intact, homogeneous
seal
, so the
diffusive path must be at least as long as the
seal
thickness. (2) Methane
diffuses through overlying strata as well as through the
seal
, and losses may
prevent gas formation. (3) Diffusive compositional fractionation reduces the
methane partial pressure below that necessary for gas formation, even after
diffusive equilibration.
The thinner the seal
, the steeper
the concentration gradient across the
seal
and the faster the diffusion.
For this reason, it has been proposed that gas forms near the base of the
seal
instead at the top of the
seal
(e. g., Prinzhofer et al., 2000). However, a
migratable gas cannot form in a homogeneous
seal
, so the diffusion path must be
at least as long as the
seal
is thick. To understand why this is so, the water
pressure and methane partial pressure distribution in the
seal
need to be
reviewed.
Water pressure at the base of the
seal
is controlled by pressure of overlying water. Shale seals are permeable to
water, but gas reservoirs at irreducible water saturation are not. Water flow in
the
seal
is caused only by its slow compaction, so its water pressure gradient
(G) is approximately hydrostatic.
If the seal
is homogeneous, its
effective diffusivity and capillary displacement pressure is the same at all
depths. The maximum methane concentration develops under steady diffusion in
equilibrium with a reservoir capillary pressure. If gas is present at
hydrostatic pressure at the top of the
seal
, the methane partial pressure
gradient is G + P/L, where L is the thickness of the
seal
and P is the capillary
pressure at the base of the
seal
(Figure 1A).
Under the most favorable conditions of steady diffusion and a positive P,
methane capillary pressure decreases up section, because G + P/L > G.
Because the
seal
is intact, the capillary pressure at the base of the
seal
is less than its capillary displacement pressure (Pd).
The capillary pressure decreases up section, whereas the displacement pressure
does not, so a gas phase cannot form in the
seal
.
Heterogeneous seals can be broken
into a series of two-layer models, where the upper layer has either greater or
lower diffusivity than the lower seal
layer.
Where the lower
seal
layer has lower diffusivity, methane capillary
pressure is less than that of the single layer case (Figure
1B). Where the upper
seal
layer has lower diffusivity, methane capillary pressure is greater than
that of the single layer case and may exceed the displacement pressure (Figure
1C). However, gas would form below the upper
seal
and could not migrate through
it, because capillary displacement pressure of the upper layer is likely to be
higher than that of the underlying layer. As
more layers are added to the model, deviations from the single layer model
become less, so it becomes less likely for the methane capillary pressure to
exceed the displacement pressure (Figure 1D).
Diffusion delivers dissolved
light hydrocarbons to strata above porous seals, but diffusion also removes
light hydrocarbons by continued upwards diffusion above the seal
.
Assume that methane is the only
light hydrocarbon diffusing upwards from a lower reservoir through a seal
into
an upper sandstone interval (Figure 2). The reservoir gas is 100 % methane at a
fixed overpressure (capillary pressure) P above
seal
hydrostatic pressure.
The
seal
is a homogeneous, porous shale with thickness L
The overlying sandstone has water-filled porosity and zero capillary
displacement pressure. The hydrostatic pressure gradient is G. Shale and upper
sandstone effective diffusivities (Dsh
and Dss, respectively) are constant
in each layer.
The reservoir layer forms the
lowest boundary for diffusion through the seal
. Methane must diffuse through the
entire
seal
thickness before a gas phase can form, because its capillary
displacement pressure is high. The partial pressure of dissolved methane at the
top of the
seal
and in the overlying sandstone is assumed to equal the water
pressure. Under these conditions, any additional methane accumulation above the
seal
will lead to gas formation.
If the water at the top of the
seal
is methane-saturated, then the maximum possible partial pressure gradient
at the top of the
seal
is the pressure difference between the top of the gas
reservoir and the base of the overlying sandstone divided by the thickness of
the
seal
(i.e., G + P/L; see Figure 2). This gradient is equal to the steady
diffusion gradient through the homogeneous
seal
.
The conditions under which gas exsolves can now be evaluated given the most favorable concentration gradients, maximum gradient into the base of the sandstone and minimum gradient away from the base of the sandstone. If a gas phase does not form under these conditions, it will not form under any conditions. Gas concentration doesn't change where the flux in and out are the same: -Dsh* (G + P/L) = -Dss*G. (negative indicates upwards flux, L is positive downward). This can be rearranged to relate the ratio of the effective diffusivity to the ratio of the concentration gradients: Dsh/Dss = G/(G + P/L). For gas to form, the flux upwards into the base of the sandstone must exceed the flux through the sandstone, so the ratio of shale effective diffusivity to sandstone effective diffusivity must exceed the ratio of the concentration gradients:
Dsh/Dss > G/(G + P/L). (1)
There are three ranges of
solutions to this inequality (Figure 3). First,
if the reservoir methane pressure is less than the water pressure above the seal
(L < |P/G| and P< 0), gas diffusion upwards through the
seal
to form a gas
is impossible because this would require a negative diffusivity, which is
impossible.
Second, if the reservoir methane
pressure is greater than the water pressure above the seal
and the overpressure
is negative (L > |P/G|, and P< 0), the effective diffusivity of the
seal
must be greater than the effective diffusivity of the overlying bed for gas to
accumulate (Dsh/Dss
> 1). Whereas this is theoretically possible, shale
seal
effective
diffusivities are experimentally determined to be lower than those of poor
quality sandstones or silts (Krooss, 1986). If this is true for all seals and
overlying coarser-grained strata, gas formation above the
seal
is not possible
under these conditions, either. Finally, where the overpressure is positive, it
is possible to exsolve a gas above the
seal
with shale diffusivity less than
that of sandstone (Dsh/Dss
< 1).
As P/L increases, the effective
diffusivity ratio required to form a gas above the seal
decreases (Figure
4).
The following conditions are typical for a typical small gas accumulation: P is
0.2 MPa (about 25 m gas column), G is 0.01 MPa/m (water density of 1 g/cc), and
L is 100 m. Under these conditions,
Dsh/Dss
is less about 0.83. In contrast,
Krooss et al. (1988) interpret permeable sandstone effective diffusivity to be
about 100 times greater than the effective diffusivity of shale (Dsh/Dss
≈ 0.01). Assuming that shale effective diffusivity is one hundredth
the sandstone effective diffusivity, overpressure of about 10 MPa and 100 MPa
would be required to form a gas phase above a 10 and 100 m
seal
, respectively.
A 10 MPa overpressure is created by a gas column about 1.2 km tall,
whereas a 100 MPa overpressure is created by a gas column 12 km tall.
Effects of compositional variation
Because methane is more soluble
and has a faster diffusivity than heavier hydrocarbons, gas exsolved from water
above the seal
will be drier than gas in the reservoir. This decreases the
likelihood for forming gas above the
seal
.
If a reservoired gas is wet, its methane partial pressure is considerably
less than the total pressure. Dry gas exsolved above the
seal
will have methane
partial pressure closer to the total pressure. The methane partial pressure
gradient must be less than the total pressure gradient, so methane diffusion
through the
seal
is slower. However, concentration gradients in beds overlying
the
seal
do not decrease, so diffusive loss does not decrease.
As a result, it is more difficult to form a gas above the
seal
.
The compositional effect can be
incorporated into a corrected methane overpressure (P*) which can be used with
Equation 1 to calculate the diffusivity ratio required for gas formation.
Consider the same reservoir-seal
-sandstone geometry of Figure
2, only now
consider the compositional change of the gas after it diffuses across the
seal
(Figure
5). Methane diffusion is
controlled by the gradient in the methane partial pressure.
Instead of methane gas exsolution at the hydrostatic pressure line, gas
exsolves where the methane partial pressure is equal to that of the exsolved
gas:
=
Ph, which will be less than the total
pressure. The corrected methane
overpressure is the pressure difference between the methane partial pressure in
the reservoir (
) and methane partial pressure of an exsolved gas above the
seal
corrected for
the difference in depth to the base of the reservoir:
. Hydrostatic pressure at the
reservoir level,
is equal to G(Z+L), while
hydrostatic pressure above the
seal
is GZ. From these relationships, the corrected methane overpressure
(P*) is the following.
(2)
Z is the depth to the top of the seal
and Xm
is the mole fraction methane in gas at the top of
seal
(t) and in the reservoir
(r). The corrected methane overpressure (P*) is substituted for P in Equation 1.
Even modest compositional changes
result in negative methane overpressure where L is small especially where the
reservoir is at great depth (Figure 4). In many cases, the methane partial
pressure is less than that of a methane-rich gas which must exsolve above the
seal
, so diffusion cannot lead to gas formation.
These
effects are shown in Figure 4, calculated from hydrostatic pressure gradient at
3 km depth, 85 % methane in the reservoired gas, and 95% methane in the exsolved
gas. Short vertical lines in the
upper right part of Figure 4 mark minimum seal
thicknesses necessary for forming
a gas phase without negative diffusivity ratios for 10 and 100 m gas columns.
Gas formation above seals thicker than these require Dsh/Dss
>1. Only where the gas column is
over 415 m thick does Dsh/Dss
become less than 1. In contrast,
all gas columns without compositional effects and with positive P have Dsh/Dss
<1.
Where low methane concentration in the reservoir is combined with high dissolved methane concentration in surrounding pore water, diffusive loss from the reservoir may stop as the concentration gradient drops to zero. This would be especially effective in very wet gases and undersaturated oils. It is even possible that methane dissolved in pore water may diffuse towards the accumulation instead of away from it (e. g., Montel et al. 1993).
Available experimental data
indicate that shale effective diffusivity is substantially lower than that of
sandstones and siltstone, so gas formation above the seal
is almost impossible
in most settings. Based on Equations 1 and 2, gas columns hundreds to thousands
of meters thick, seals less than 10 m thick, and very dry reservoired gases are
needed to form a gas above the
seal
, if diffusivity ratios similar to
experimental values are chosen. These
conditions are rare, so settings where diffusion by itself forms a gas above
seals are expected to be rare.
Special circumstances may be
imagined where the seal
/sandstone effective diffusivity ratio is significantly
larger than 0.01. The easiest way
is to decrease the reservoir quality of the overlying unit, which will increase
its tortuosity and decrease its effective diffusivity. However, this has the side effect of increasing the rock
capillary displacement pressure, so higher gas partial pressure is required to
form a mobile gas. If a mobile gas
phase does not form, the diffusive path length increases, concentration gradient
decreases and diffusive flux decreases. The net result of decreasing reservoir quality of beds
overlying the
seal
is to thicken the
seal
.
Another possible setting is where
beds overlying the seal
are overlain by another
seal
which limits its diffusive
loss. This problem is similar to
the heterogeneous
seal
already considered.
The shallower
seal
also has diffusive loss. Rate of diffusive loss through the shallow
seal
will be
similar to that of the deep
seal
unless the shallower
seal
has a lower effective
diffusivity or greater thickness. Except in cases of obvious thickness
variations, it is difficult to judge which
seal
would have the higher diffusive
loss. Decreasing temperature up
section decreases diffusivity whereas greater porosity at shallower depths will
increase effective diffusivity.
Of course, there are other geological settings in which dissolved gases can exsolve. The two most obvious are recently exhumed basins and areas of resurgent subsurface waters (e. g., Cramer et al., 1999). As total pressure decreases, light hydrocarbons dissolved in pore water exsolve, and gas can then migrate to fill traps. Both settings are easily recognized by the geologist, so areas with potential for diffused gases might be predicted even before sampling. Even in these settings, solubility fractionation of light hydrocarbons will probably exceed diffusive fractionation, because all exsolved gas will have fractionated during dissolution and exsolution, whereas only some of the exsolved gases will have diffused from reservoirs.
Cramer, B., H. S. Poelchau, P. Gerling, N. V. Lopatin, and R. Littke, 1999, Methane released from groundwater: the source of natural gas accumulations in northern West Siberia: Marine and Petroleum Geology, v. 16, p. 225-244.
Garrels, R. M. and C. L. Christ, 1965, Solutions, Minerals, and Equilibria: Harper and Row, New York, 450 p.
Krooss, B. M, 1986, Diffusion of C1 to C5 hydrocarbons in water-saturated sedimentary rocks: Erdöl und Kohle - Erdgas - Petrochemie, v. 39, p. 399-402.
Krooss, B. M., D. Leythaeuser, and R. G. Schaefer, 1988, Light hydrocarbon diffusion in a caprock: Chemical Geology, v. 71, p. 65-76.
Montel, F., G. Caillet, A. Pucheu, and J. P. Caltagirone, 1993, Diffusion model for predicting reservoir gas losses: Marine and Petroleum Geology, v. 10, p. 51-57.
Prinzhofer, A., M. R. Mello, and T. Takaki, 2000, Geochemical characterization of natural gas: a physical multivariable approach and its applications in maturity and migration estimates: Bulletin AAPG, v. 84, p. 1152-1172.
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