Seal capacity estimation from subsurface pore pressures
Descripción
Basin Research (2005) 17, 583–599, doi: 10.1111/j.1365-2117.2005.00281.x
Seal capacity estimation from subsurface pore pressures Hege M. Nordga˚ rd Bola˚ s, Christian Hermanrud and Gunn M. G. Teige Statoil ASA, Research Centre,Trondheim, Norway
ABSTRACT A cap rock’s capacity to seal hydrocarbons depends on its wettability and the sizes of the pore throats within the interconnected pore system that the leaking hydrocarbons must penetrate.These critical pore throat sizes are often poorly constrained in hydrocarbon exploration, partly because measurements of pore throat sizes have not been performed, and partly because pore throat measurements on a few individual samples in the cap rock may not be representative for the seal capacity of the top seal as a whole. To the contrary, the presence of formation overpressure can normally be estimated in drilled exploration targets.The presence of overpressure in reservoirs testi¢es to small pore throats in the cap rocks, as large pore throats will result in su⁄ciently high cap rock permeability to bleed o¡ the overpressure. We suggest a stepwise procedure that enables quanti¢cation of top seal capacities of overpressured traps, based on subsurface pressure information.This procedure starts with the estimation of cap rock permeabilities, which are consistent with observed overpressure gradients across the top seals. Knowledge of burial histories is essential for these estimations. Relationships between pore throat size and permeability from laboratory experiments are then applied to estimate critical pore throat diameters in cap rocks.These critical pore throat diameters, combined with information of the physical properties of the pore £uids, are then used to calculate membrane seal capacity of cap rocks. Estimates of top seal capacity based on this procedure are rather sensitive to the vertical £uid velocity, but they are also to some extent sensitive to inaccuracies of the pore throat/permeability relationship, overpressure gradient, interfacial tensions between pore £uids, hydrocarbon density and water viscosity values. Despite these uncertainties, applications of the above-mentioned procedure demonstrated that the mere presence of reservoir overpressures testi¢es to su⁄cient membrane seal capacity of cap rocks for most geological histories. Exempt from this statement are basins with rapid and substantial sediment compaction in the recent past.
INTRODUCTION
where
A trap’s capacity to retain hydrocarbons is either limited by its structural spill point or the seal capacity of its boundaries (top, side and bottom seals). Such boundaries may either act as membrane seals or as hydraulic seals (Watts, 1987). The seal is de¢ned as a membrane seal if hydrocarbons £ow through the water-wet seal when the hydrocarbon column height exceeds a critical value, whereas the seal is classi¢ed as a hydraulic seal if the capillary entry pressure is so high that fractures are needed for hydrocarbons to escape. The maximum column height that can be preserved by membrane seals is attained when the buoyancy of the hydrocarbon column equals the capillary entry pressure (Berg, 1975):
Pce ¼ 4g=d:
Drgh ¼ Pce
ð1Þ
Correspondence: Hege M. Nordgrd Bols, Statoil ASA, Research Centre, N-7005 Trondheim, Norway. E-mail: hnb@ statoil.com r 2005 The Authors. Journal compilation r 2005 Blackwell Publishing Ltd
ð2Þ
Here, Dr is the density contrast between water and hydrocarbons, g is the acceleration due to gravity, h is the maximum hydrocarbon column height, Pce is the capillary entry pressure, g is the interfacial tension between hydro carbon and water, and d is the diameter of the pore throats in the cap rock. The term cos y is often included at the right-hand side of Eqn. (2), where y is the contact angle between the hydrocarbon boundary and the water that coats the solid surface (as measured through the more dense £uid). However, when breakthrough of hydrocarbons occurs, the angle between the surface of the grain and the hydrocarbons is zero (cos y 5 1).The maximum hydrocarbon column height h will be referred to as the seal capacity in the forthcoming text. The accuracy of membrane seal capacity predictions depends on the ability to determine the £ow paths for hydrocarbon escape through the seal. These £ow paths
583
H. M. Nordgrd Bols et al. comprise the largest interconnected pores, and the hydro carbon escape will be limited by the sizes of the smallest pore throats within these £ow paths.The diameter of these pore throats, hereafter referred to as the critical pore throat diameter dc, may be estimated from analyses of pore size distributions based on mercury injection experiments. Unfortunately, adequate sample material for such analyses are often not available, and the representativeness of any analyses based on such small individual rock samples to the critical pore throats of thicker and much more lateral extensive units will always be open to speculation. However, indirect information on seal capacity is available if formation overpressures are present. According to Darcy’s law, overpressures result when the transmissibilities of all the boundaries of a pressure compartment are su⁄ciently low to cause a reduction in the £uid £ux out of the compartment. The transmissibility of a seal is largely controlled by its permeability, which can be estimated from the mean pore diameter. Amyx et al. (1960) suggested a quantitative relationship between these quantities, and Krushin (1997), Schl˛mer & Krooss (1997), Katsube et al. (1998) and Y. L. Yang & A. C. Aplin (submitted) provided measurements of cap rock permeabilities and pore throat sizes that can be applied to determine re¢ned relationships between these two parameters. Relationships between overpressure gradients through a seal and pore throat diameters on the one hand, and that of pore throat diameters and seal capacity on the other hand, suggest that quanti¢cation of seal capacity should be possible based on the knowledge of subsurface pore pressures. This paper aims at deriving such a quantitative relationship and on providing order- of-magnitude estimates of top seal capacities that can be inferred from observed overpressures in basins of various geological histories. Even if the proposed method depends on subsurface pressure information, it can also aid in the prediction of seal capacity in undrilled targets. If a particular top seal unit has demonstrated the ability to preserve signi¢cant overpressures in one location (i.e. an overpressure gradient through the cap rock is detected by drilling), then similar reduced seal transmissibilities and related seal capacities can be a possibility in other areas where the same top seal unit is present and comparable top seal characteristics are expected. Also, seal capacities can be predicted directly from reliable subsurface pore pressure prognoses.
seals, then the trap capacity will be less than or equal to the seal capacity of the cap rock. For this reason, calculated top seal capacities will always produce maximum estimates of the trap capacity in pressure compartments. Estimating top seal capacity from subsurface £uid overpressures will require parameters that are not accurately known, and simplifying assumptions are invoked in order to derive estimates of these parameters. Although the most likely parameter values will serve as a basis for the discussion of the sensitivity of the top seal capacity estimates, efforts have been made to ensure that the simpli¢cations drive the calculated top seal capacities towards low values. We select this approach to ensure that, when our procedure results in a calculated top seal capacity of a certain column height, the top seal is capable of preserving this column height or even more. The calculation of minimum top seal capacity will be performed as a three- stage process: (a) calculation of top seal permeabilities from subsurface £uid pressures and £ow rates, (b) calculation of critical pore throat diameters from top seal permeabilities and (c) calculations of top seal capacities from critical pore throat diameters. This work£ow is illustrated in Fig. 1.
Calculation of top seal permeability from subsurface fluid pressures The relationship between £uid £ow velocity and overpressure gradient in a porous medium is given by Darcy’s law: V ¼ fU ¼ m1 KHPe
where V is Darcy velocity, f porosity, K the permeability tensor, m £uid viscosity and HPe the overpressure gradient. Note that the Darcy velocity is not the true velocity (U) of the £uids relative to the subsiding grains, but the velocity the moving £uids would have if they did not £ow in a porous medium. Darcy’s law enables the calculation of the vertical cap rock permeability provided that water viscosity, vertical overpressure gradient and vertical £uid velocity are known. Water viscosity Water viscosity reduces with increasing temperature and burial depth.Weast & Astle (1982) give the relationship m ¼ 10n
ð4Þ
SEAL CAPACITY CALCULATED FROM FLUID OVERPRESSURES
where
This study addresses the seal capacity of top seals. In our study, we de¢ne the term ‘top seal’ to be equivalent to ‘cap rock’. If the top seal quality limits the hydrocarbon column height within a pressure compartment, then the top seal capacity is equal to the trap capacity. If the hydrocarbon column height of such a trap is limited by side or bottom
n ¼ ð1:3272ðT 20Þ 0:001053ðT 20Þ2 Þ=ðT þ 105Þ:
584
ð3Þ
ð5Þ
Here, m is given in centipoises (cp) and T is temperature in 1C. According to this relationship, the water viscosity is 1cp forT 5 20 1C and about 0.3 cp forT 5 100 1C (Fig. 2). r 2005 Blackwell Publishing Ltd, Basin Research, 17, 583^599
Seal capacity estimation Ob flu serve id pre d ssu re
Seal Numerical Permeability/pore throat Seal basin modelling permeabilities relationships pore throats
l ria Bu y tor his
Buoyancy vs. Membrane capillary entry pressure seal capacity relationship
Fig. 1. Generalized work£ow for membrane top seal capacity estimation based on subsurface £uid pressure observations.
0
Water viscosity (cp) 1 1.5 0.5
2
0 20 40
Temperature (°C)
60 80 100 120 140 160 180 200
Fig. 2. Water viscosity vs. temperature relationship. From Weast & Astle (1982).
Vertical overpressure gradient Throughout this study, we de¢ne the vertical overpressure gradient to be related to the pressure in the water phase only. The vertical overpressure gradient across a seal is safest estimated from well data. The vertical overpressure gradient is the di¡erence between the overpressure gradient at the top and the overpressure gradient at the base of this seal: DP=DZ ¼ ððP Ph Þbase ðP Ph Þtop Þ=ðZbase Ztop Þ: ð6Þ
Here, DP/DZ is the vertical overpressure gradient, P is the pore pressure of the water phase, Ph is the hydrostatic pore pressure and Z is the depth (here de¢ned positive downwards).The subscripts at the top and the base denote the top and base of the cap rock.The cap rock is de¢ned as the rock sequence that immediately overlies the reservoir rock, and which has a well-de¢ned overpressure gradient here. The pore pressure at the base of the seal will in this procedure be the same as the pore pressure of the water phase at the top of the underlying reservoir. In an undrilled exploration target, the overpressure gradient can be predicted from a variety of methods, but it is best estimated from extrapolation of nearby well data, where the r 2005 Blackwell Publishing Ltd, Basin Research, 17, 583^599
cap rock sequence is the same as in the prospect of investigation. Vertical £uid velocity The vertical £uid velocity in a basin is the least well- constrained parameter that is required for calculations of cap rock permeability, as no direct measurements of this parameter exist. Whereas the physical signi¢cance of the true £uid velocity (U ) can be easily appreciated, it is the Darcy velocity (V ) that is most conveniently applied in £uid £ow calculations, because this velocity is continuous across boundaries of strata with di¡erent porosities. The forthcoming discussions of the relationships between overpressures and hydrocarbon column heights will therefore be based on analyses of Darcy velocities. The simplest way to estimate vertical £uid velocity is to assume that porosity vs. depth relationships in entire basins do not vary with time. In such situations, the sediments can be visualized as moving through a standing body of water during subsidence (Bonham, 1980). This suggestion implies that the true £uid velocity (U ) equals the burial rate of the sediments at the top of the sedimentary pile, which again is close to the age of the youngest sedimentary package divided by the time span of its formation. The Darcy velocity (V ) in these shallow sediments can then be calculated by multiplying the true velo city with the average porosity of the sediments. Estimates of the Darcy velocity at greater depths can be found by compensating the burial rate for compaction of the overlying rocks. However, the porosity reduction rates depend not only on the burial rate, but also on factors such as lithology, heating rate and compaction process. These factors will therefore signi¢cantly in£uence the subsurface £uid £ow as well. Compaction of argillaceous rocks is believed to be largely an e¡ective stress-driven process at low temperatures and shallow burial depths (Dewhurst et al., 1998). In this setting, overpressures will inhibit further porosity reduction with reduced £uid velocity as a result. The porosity reduction rate will thus not accurately re£ect the subsidence rate, although it will be correlated with the burial rate over prolonged time periods. Several studies (Bjrkum,1996; Oelkers etal.,1996;Teige et al., 1999; Nordgrd Bols et al., 2004) have however demonstrated that compaction of clastic rocks is largely chemical and controlled by temperature at moderate-to -deep burial, and that e¡ective stress has a subordinate role here.
585
H. M. Nordgrd Bols et al.
Sandy sediments
Shaly sediments
Directions of fluid flow
Fig. 3. Generalized £uid £ow patterns on a basin scale.The £uids move upwards and laterally towards the £anks of the basin relative to the subsiding sediments. As a result, one-dimensional £uid £ow modelling will overestimate the vertical £uid £ow on average.
Although rapid burial may lead to a rapid increase in temperature and thus accelerated chemical and stress-insensitive porosity reduction, such temperature-driven porosity reduction is also time dependent. The contribution to the vertical £uid £ow from thermally driven porosity reduction will thus be correlated with burial rate, but will also depend on other factors such as the volume of porous rocks that are exposed to the increased temperature and to the porosity of these rocks prior to the increased heating. The above considerations dictate that numerical basin modelling should be performed in order to bracket the porosity reduction rate in the forthcoming seal capacity calculations. Such modelling results in modelled £uid £ow velocities that is a response to the modelled compaction history of the sediments. The compaction modelling relies on (often empirical) relationships between porosity and e¡ective stress, and/or porosity reduction vs. temperature relationships. The calculated e¡ective stress is in£uenced by assumed relationships between permeability and factors such as porosity and speci¢c surface area. Despite the uncertainties involved in these calculations, modelled £uid velocities are often quite robust, because parameters in these empirical equations are calibrated to match observed porosity and £uid pressure data in wells. The most critical factors involved in modelling of £uid velocity are (a) knowledge of the compaction mechanism and (b) correct estimation of the relative magnitudes of £uid £ow in various directions: (a) Modelling based on e¡ective stress-driven compaction will result in lower modelled vertical £uid £ow than what will be the case with stress-insensitive compaction modelling. As is clear from Eqn. (3), low £uid velocities require correspondingly low permeabilities to sustain a ¢xed overpressure gradient. Modelling based on thermally driven, stress-insensitive compaction at moderate and high temperatures will therefore result
586
in comparatively higher estimated cap rock permeabilities and more pessimistic seal capacity calculations than those that would result from modelling of e¡ective stress-driven compaction only. We have included chemical compaction in our modelling, as this mechanism ensures calculations of the highest £uid velo cities and hence high- side permeability and related low- side seal capacity estimates. (b) The vertical component of subsurface £uid £ow is not easily determined. Fluids may be transported to and from pressure compartments both in pore networks and in fractures, and laterally as well as vertically. Quanti¢cation of the relative proportions of £uid £ow across all a compartment’s boundaries would require knowledge of the ratio between the permeabilities of all these boundaries. Such information is clearly not available, although it can be constrained by three-dimensional (3D) basin modelling calibrated to a set of pressure measurements in nearby wells.The processes that lead to porosity reduction can however be adequately addressed by 1D basin modelling. This is possible because both the mechanical and thermal processes that lead to porosity reduction are largely 1D. To the contrary, subsurface £uid £ow is 3D. However, the overall lateral £uid £ow in sedimentary basins is directed from the deepest central areas towards the shallower £anks of the basin (Fig. 3). This observation suggests that calibrated1D £uid £ow modelling will on average overestimate the vertical £uid £ow relative to the sediment grains.When permeabilities are adjusted to match the observed overpressures during modelling, overestimated vertical £uid £ow will result in calibrated vertical permeability values that are too high. As a result, too large pore throat sizes and too pessimistic seal capacities will be estimated. We perform 1D modelling to estimate the vertical £uid £ow velo city in this paper, and realize that this approximation will result in low- side seal capacity estimates. r 2005 Blackwell Publishing Ltd, Basin Research, 17, 583^599
Seal capacity estimation (a) 10−1
Viscosity = 0.3 cp (deep burial)
Permeability (mD)
10−2 10−3
V=1
10−4
V=1
10−5
V=1
10−6
V=1
10−7
V=0
10−8
V=0
10−9
V=0
000 00
0
.1 .01
.001
10−10 10−11 10−1
1
102
10
103
Overpressure gradient (MPa/km) (b) 10−1
Viscosity = 1 cp (shallow burial)
10−2
V=1
000
Permeability (mD)
10−3
V=1
00
10−4
V=1
0
10−5
V=1
10−6
V=0
.1
10−7
V=0
.01
10−8
V=0
.001
10−9 10−10 10−11 10−1
1
10
102
103
Overpressure gradient (MPa/km)
Fig. 4. Top seal permeability as a function of the overpressure gradient across the seal for a variety of Darcy velocity values (V) in m Myr^1, (a) for viscosity m 5 0.3 cp (deep burial) and (b) for viscosity m 5 1.0 cp (shallow burial).
Vertical cap rock permeability For practical purposes, Darcy’s law can be rearranged as kz ¼ 3:2 105 Vz m=ðDP=DZÞ:
tween permeability and pore throat sizes of cap rocks. We have applied four laboratory experiment data sets for this purpose.
ð7Þ The Schl˛mer & Krooss (1997) data set
This rearrangement allows for calculation of vertical permeability (kz) in mD, where the vertical Darcy velocity Vz is measured in m Myr^1, water viscosity m is given in cp and the overpressure gradient DP/DZ is given in MPa km 1, with Z de¢ned as positive downwards.This relationship between vertical permeability, overpressure gradient and Darcy velocity is displayed graphically in Fig. 4, where both (a) deeply buried (m 5 0.3 cp) and (b) shallowly buried (m 5 1.0 cp) sediments are represented.
Calculation of critical pore throats diameters from top seal permeability Having established a procedure for the estimation of cap rock permeability from observed overpressure gradients across cap rocks, we proceed to examine relationships ber 2005 Blackwell Publishing Ltd, Basin Research, 17, 583^599
Schl˛mer & Krooss (1997) measured permeabilities for 27 Jurassic shale and mudrock samples from the Haltenbanken area o¡shore Norway and from Carboniferous and Permian red claystones of northern Germany. The permeabilities of the 23 samples that were considered ‘realistic’ by the authors varied between 6 10 7 and 4 10 3 mD. The authors also listed the mercury displacement pressures for these samples. The displacement pressure is de¢ned as the pressure required to form a continuous ¢lament of nonwetting £uid through the largest interconnected pore throats of the rock. The pore throats corresponding to the displacement pressure are therefore equal to the critical pore throat diameter (dc).The displacement pressure is further de¢ned as the intersection of the tangent to the in£exion point of the sigmoidal capillary
587
H. M. Nordgrd Bols et al.
Critical pore throat diameter (nm)
105
104
plin
Eq.
103
10
ng (Ya
&A
95) d) y (19 itte Aver d n a Berg 992) an (1 Pittm
bm , su
)
97 oss, 19 r & Kro chlöme ) 8 (S 9 9 9 1 . Eq t al., atsube e Eq. 12(K
102
10
1 10 −1 10 −8
10 −7
10 −6
10 −5
10 −4 Permeability (mD)
10 −3
Katsube et al. (1998)
Yang & Aplin (submitted)
Schlömer & Krooss (1997)
Krushin (1997)
10 −2
10 −1
Fig. 5. Critical pore throat diameter vs. permeability relationships in shaly cap rocks, based on data from Krushin (1997), Schl˛mer & Krooss (1997), Katsube et al. (1998) and Yang & Aplin (submitted), displayed together with calculated regression lines for each relationship.The sandstone relationships of Berg & Avery (1995) and Pittman (1992) are included to illustrate the consistency between shale and sandstone models.
pressure curve with the logarithmic pressure axis (Schl˛ mer & Krooss, 1997). According to Schl˛mer & Krooss (1997), the samples are at displacement pressure when approximately 10% of the pores have been saturated with the nonwetting £uid. We relate this mercury displacement pressure (Pci) to the equivalent critical pore throat diameter dc by dc ¼ 4g cos y=Pci
ð8Þ
where g is the interfacial tension between mercury and air (0.471 N m 1) and y is the wetting angle between mercury and air (1401). The resulting permeability/pore size data pairs from Schl˛mer & Krooss (1997) are plotted in Fig. 5 together with the corresponding regression line Log dcS ¼ 0:3085 Log k þ 3:0103;
R2 ¼ 0:4798
ð9Þ
where dc is the critical pore throat diameter (nanometers), the subscript ‘S’ denotes Schl˛mer & Krooss (1997) and k is permeability (mD). R2 is the coe⁄cient of correlation. TheYang & Aplin (submitted) data set A total of 45 mudstone samples were measured for permeability (both horizontal and vertical) vs. pore throat size relationships by Yang & Aplin (submitted).The samples were taken in the depth range from about 1000 to 5000 m in the North Sea, the Gulf of Mexico and the Caspian Sea. Both the mean pore size diameter, which equals the 50% precentile (d50: 50% of the pores were larger than this value) and the 10% percentile (d10: 10% of the pores were larger
588
than this value) were noted from the 38 samples where the measurements were judged as good or moderate by the authors. The rest of the measurements were described as poor and are excluded from our analysis. The d10 data should be directly comparable with the pore throat diameters that were calculated from the displacement pressures provided by Schl˛mer & Krooss (1997), as the d10 data should provide close approximations of the critical pore throat diameters of the samples (d10 5 dc).The d10 data of Yang & Aplin (submitted) range from 10 to 1000 nm, with the corresponding permeabilities ranging from 5 10 7 to 3 10 3 mD. These data are shown in Fig. 5 together with the related linear regression line, with the subscript ‘Y’denoting Yang & Aplin (submitted): Log dCY ¼ 0:7187 Log k þ 5:5655;
R2 ¼ 0:8970: ð10Þ
The Katsube et al. (1998) data set Katsube et al. (1998) presented 22 measurement pairs of pore- size mode distribution vs. permeability for shale samples from the Venture gas ¢eld (o¡shore Nova Scotia), the Beaufort-Mackenzie Basin (North^West Territories) and the Western Canada Basin.The permeabilities of these samples were reported to be approximately in the 10 7^ 10 4 mD range, and the pore- size distributions were all unimodal. As the mode of the pore- size distribution (dm) is equal to the mean pore size (d50) for unimodal pore size distributions, the pore size modes of Katsube et al. (1998) r 2005 Blackwell Publishing Ltd, Basin Research, 17, 583^599
Seal capacity estimation are smaller than the size of the critical pore throats (dmodc). The pore- size mode distributions of Katsube et al. (1998) are therefore not directly comparable with the critical pore sizes reported by Schl˛mer & Krooss (1997) or Yang & Aplin (submitted). Figure 6 shows the relationship between the d10 and the d50 data from Yang & Aplin (submitted). In this ¢gure, d10 is plotted as a function of d50 together with the linear regression line
ð11Þ We applied this relationship to convert the mode poresize values reported by Katsube et al. (1998) to corresponding estimates of critical pore throats (dc), in order to make this data set consistent with the other data sets. Here, we
105
8)
.26
+0
d10 (nm)
og
l 39
103
d 50
ð12Þ
All data sets Krushin (1997) reported permeability and displacement pore throat sizes for eight non- smectitic shale samples. These data are also shown in Fig. 5. A separate regression line through these data is however not displayed, because of the limited permeability range they span (4.2 10 6 to 7.3 10 6 mD). However, a linear regression line through all the four above described data sets was calculated (Fig. 7), giving an expression of the calculated critical pore throat diameters based on all compiled data (dcAll) as
,01
=1 0 gd1
102 10
R2 ¼ 0:2934:
Log dcK ¼ 0:2454 Log k þ 2:6099;
R2 ¼ 0:9727:
Log d10 ¼ 1:0139 Log d50 þ 0:268;
104
assume that this relationship based on the shales studied by Yang & Aplin (submitted) also has a fair validity for the shales studied by Katsube et al. (1998). The adjusted data from Katsube et al. (1998) are plotted in Fig. 5, together with the following linear regression line, where the subscript ‘K’denotes Katsube et al. (1998)
R2 ¼ 0:4359:
Log dcAll ¼ 0:4295 Log k þ 3:8013;
lo 1(
ð13Þ
.1
Eq
1 10 −1 10 −1
10
1
102
103
104
105
d50 (nm)
Fig. 6. Relationship between the critical (d10) and the mean (d50) pore throat diameters of Yang & Aplin (submitted).This relationship was used to convert the mode of the pore throat distribution (dm) of Katsube et al. (1998) into the corresponding critical pore throat diameters (d10).
The relationships between critical pore throat size and permeability that emerge from the various data sources vary signi¢cantly (Figs 5 and 7), especially for the comparatively high permeability samples. For comparison, we have included the critical pore throat size/permeability relationships for sandstones from Pittman (1992) and Berg & Avery (1995) towards the high-permeability end of these ¢gures.These predictions fall between those of the various shale data, and do not favour any speci¢c data set: the Berg & Avery (1995) relationship ¢ts quite well with the data
Critical pore throat diameter (nm)
105 very
dA rg an
104
5)
(199
Be
992)
an (1
Pittm
103 3 (All
Eq. 1
es)
sourc
102 10
1 10 −1 10 −8
10 −7
10 −6
10 −5
10 −4
10 −3
10 −2
10 −1
Permeability (mD)
Fig. 7. The relationship between critical pore throat diameter and permeability, based on all the available data in Fig. 5, displayed with the resulting regression line. r 2005 Blackwell Publishing Ltd, Basin Research, 17, 583^599
589
H. M. Nordgrd Bols et al. from Yang & Aplin (submitted) (Fig. 5), whereas the Pittman (1992) curve closely matches the regression line based on all available data (Fig. 7).We also note that the data from Yang & Aplin (submitted) (Fig. 5) display less variation in pore throat size/permeability relationships than the other data sets, and that they result in higher estimated pore throat sizes than the other data (including those of Krushin, 1997). Whether this observation indicates a more homogeneous sample set or has some other explanation is unknown.
Calculation of top seal capacity from critical pore throat diameters The seal capacity of a water-wet cap rock can be calculated once the size of the critical pore throat is known, as Eqns (1) and (2) give h ¼ 4g=Drgdc
ð14Þ
where dc is the diameter of the critical pore throat. Application of this equation to hydrocarbon exploration requires knowledge of the hydrocarbon density and the interfacial tension between the pore £uids. These properties should be estimated for the individual prospect or play under consideration. However, for the purpose of deriving order-of-magnitude estimates of seal capacities inferred from observed overpressures, we ¢nd it useful to address the relationships between these variables and burial depth/temperature for di¡erent hydrocarbon types.
Hydrocarbon density Watts (1987) published overpressured and normally pressured gas (methane) density data related to burial depth. At great depths and high temperatures, natural gases may have much higher densities than pure methane. However, by using density data for dry gas in our calculations, we ensure that low- side values of seal capacity of gas are calculated. Watts (1987) also published oil density data, but he did not show how such data typically vary with depth or temperature. To exemplify such a data set, density data for 13 northern North Sea oil ¢elds with GOR ranging from 50 to 300 Sm3 Sm 3 (from Spencer et al., 1987) are displayed together with the Watts (1987) gas data in Fig. 8. Interfacial tension The interfacial tensions between subsurface hydrocarbons and water vary signi¢cantly with the hydrocarbon compo sition, the gas oil ratio, the presence of organic acids and the presence of contaminants. As a result, generalized relationships between interfacial tensions and other parameters such as burial depth or temperature will be highly uncertain, and the interfacial tension should be calculated for the individual hydrocarbon type that is expected in the reservoir. We nevertheless need generalized relationships for the forthcoming discussions of sensitivity of the calculated seal capacities. Several authors have measured and computed interfacial tensions between water and pure hydrocarbons at reservoir temperature and pressure conditions, including methane, propane, n-butane, n-pentane, n-hexane, nheptane, n- octane, n-dodecane and benzene. Hocott
Density (g/cm3) 0.1
0.2
0.3
0.4
0.5
0.6
0.7
Depth (meters)
2500
40
l
60 Oi
s ga red su s ga res erp red Ov ssu pre ally
2000
1
20 rm No
1500
0.9
7
500 1000
0.8
80 100
3000 120
Temperature (°C)
0 0
3500 140 4000 4500 5000
160 180
Fig. 8. Oil and gas density vs. burial depth and temperature.The relationship between burial depth and temperature is based on a temperature gradient of 35 1C km 1 and a surface temperature of 7 1C.The gas data are from Watts (1987), whereas the oil data were compiled from 13 northern North Sea oil ¢elds described in Spencer et al. (1987).
590
r 2005 Blackwell Publishing Ltd, Basin Research, 17, 583^599
Seal capacity estimation (1939), Hough et al. (1951), Jennings & Newman (1971) reported interfacial tensions for methane^water systems at various temperatures and pressures. Hassan et al. (1953), Aveyard & Haydon (1965), McCa¡ery (1972) and Watts (1987) all described interfacial tensions for various types of the heavier hydrocarbon components. The representativeness of these data to subsurface conditions is uncertain, as all of these data were based on re¢ned hydrocarbons. Also, some of the experimental techniques used (e.g. organic seals in testing equipment) were likely to have a¡ected the accuracy of these early research e¡orts (Boult et al., 2003). Firoozabadi & Ramey (1998), however, presented correlations for calculating interfacial tension for pure and mixed hydrocarbon types that were also calibrated against measured data. We have used these correlations to calculate interfacial tensions for oil and gas as a function of burial depth. The diagram of Firoozabadi & Ramey (1998; their Fig. 6), which show interfacial tensions between pure methane and water as a function of density and temperature, can be described by the following formula: 0:3125 gm ¼ ð3:337Dr0:261 Þ m =Tr
4
tween oil and water, can be described by 4
Þ: go ¼ ð2:6562Dr0:0857 o
Here, go is the interfacial tension between oil and water and Dro is the density contrast between oil and water.This relationship does partially include the e¡ect of temperature for oil, as the data were obtained over a temperature range of 571^105 1C and all these data fell on one line. These data were acquired over a pressure range of 0.5^ 38 MPa. However, Firoozabadi & Ramey (1998) did not account for brine salinity, which apparently does a¡ect the results, but not in a major fashion. Here, we emphasize that interfacial tension for oil in the subsurface is notoriously di⁄cult to estimate, as oil composition has a significant in£uence and can be very variable spatially. Equations (15) and (17) were combined with the density vs. depth/temperature relationships of gas and oil of Fig. 8 to give the interfacial tension vs. depth curves of Fig.9. Figure 9 suggests that gas has a higher interfacial tension than oil at shallow burial, and that the di¡erence between the two reduces with burial depth. Also, the relationships of Firoozabadi & Ramey (1998) imply that the interfacial tension of oil actually exceeds that of gas at larger depths.This result appears to be counter-intuitive, and may possibly be an artefact of applying pure methane as an analogue for subsurface gas accumulations and of the above-mentioned uncertainties in determination of interfacial tensions for oil^water systems, including the use of gassaturated natural oils for subsurface oil accumulations. We consider this issue no further, and acknowledge that application of laboratory-derived interfacial tension data (including those of Firoozabadi & Ramey, 1998) to subsurface conditions does introduce uncertainties to the seal capacity calculations.
ð15Þ
where Tr ¼ 0:0053T þ 1:4285:
ð16Þ
Here, gm is the interfacial tension between methane and water, Drm the density contrast between methane and water, Tr the reduced temperature and T the temperature ( 1C). For simplicity, we allow pure methane to represent the gas case in our following calculations. Another diagram of Firoozabadi & Ramey (1998; their Fig. 10), which shows interfacial tension between crude oil and water solely as a function of the density contrast be-
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Fig. 9. Oil and gas interfacial tension calculated from the relationships established by Firoozabadi & Ramey (1998).The oil and gas density vs. burial depth relationships of Fig. 8 were used to display the interfacial tensions vs. burial depth. r 2005 Blackwell Publishing Ltd, Basin Research, 17, 583^599
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H. M. Nordgrd Bols et al. Table 1. Typical £uid properties for shallow burial (1km), intermediate burial (2.5 km) and deep burial (4 km for oil and 5 km for gas) based on the data in Figs 8 and 9
Shallow oil Intermediate deep oil Deep oil Shallow gas Intermediate deep gas Ultradeep gas
Depth (m)
Temperature ( 1C)
Hydrocarbon density (g cm 3)
Interfacial tension (mN m 1)
1000 2500 4000 1000 2500 5000
42 94.5 147 42 94.5 182
0.80 0.67 0.51 0.07 0.20 0.23
29 34 39 61 43 29
A geothermal gradient of 35 1C km 1 and a surface temperature of 7 1C were used to convert temperatures to depths. Density values for normally pressured gas were used for the shallow gas, whereas density values for overpressured gas were used for the intermediate to ultra deep gas. Fluid pressure at 80% of the lithostatic stress was assumed for the overpressured case.
10 5
Shallow oil (1 km)
Hydrocarbon column height (m)
Oil (2.5 km)
10 4
Deep oil (4 km)
10 3
Gas (2.5 km)
Shallow gas (1 km)
Ultra deep gas (5 km)
10 2 10 1 10 −1 10 −2 1
10
10 2
10 4
10 3
10 5
10 6
Pore throat diameter (nm)
Fig. 10. Seal capacity calculated from estimates of the critical pore throat diameter and £uid properties (density and interfacial tension) of the reservoired hydrocarbons.
Seal capacity As a basis for the discussions of general sensitivity and accuracy of the seal capacity estimations, typical £uid prop erties for shallow, intermediate and deep oil and gas accumulations are compiled in Table 1. These values were used to generate Fig. 10, which visualizes calculated seal capacities based on Eqn. (14). As is seen from this ¢gure, oil is more easily retained than gas for a given cap rock, and shallow hydrocarbon accumulations are more easily retained than deep ones. A ¢gure similar to Fig. 10 was provided by du Rouchet (1984). His conclusions were however signi¢cantly less op timistic with respect to seal capacity than those that emerge from our work.The small seal capacities advocated by du Rouchet (1984) mainly resulted from his anticipation of pore throat diameters in the 1000^2000-nm range. As shown in Fig. 5, several later investigations have demonstrated that pore throat diameters of shaly cap rocks are commonly less than 100 nm, and occasionally even less
592
than 10 nm. As a result, the seal capacity estimates of du Rouchet (1984) should be considered as outdated.
ACCURACY AND SENSITIVITY OF SEAL CAPACITY CALCULATIONS The suggested three- step process for seal capacity calculations from subsurface pressure data, as described in the previous sections of this paper, involve a number of assumptions and approximations that introduce uncertainties to the calculated seal capacity. As a basis for analysing these uncertainties, we selected two case studies to demonstrate situations (1) where the proposed method of seal capacity estimation from subsurface pore pressures will give large estimates of seal capacity, and (2) where small seal capacities will be estimated from subsurface pore pressures. Our proposed method will generally estimate the smallest seal capacities in cases where £uid r 2005 Blackwell Publishing Ltd, Basin Research, 17, 583^599
Seal capacity estimation velocities are high, which will be the situation if the sediments compact rapidly (i.e. mechanical compaction because of rapid subsidence at shallow depths, and chemical compaction because of sediment exposure to high temperatures at deeper burial). First, we describe these case studies and calculate the seal capacity based on our judgement of the most likely input parameters. Second, we discuss the uncertainties related to our suggested procedure of calculating seal capacity from overpressure gradients, which include sensitivities of each individual input parameter required for the calculations, the choice of permeability vs. pore throat relationship and the e¡ects of changes in capillary pressures.
Case studies: Norwegian North Sea (case 1) and Eugene Island Basin (case 2) As case 1, we select Well 34/10 -35 in the Norwegian North Sea. This well is located in the North Viking Graben area and penetrates the Gullfaks Gamma fault-block structure south of the Gullfaks Field (Nordgrd Bols et al., 2004). The well encountered a 29-m gas column in a gas-downto situation in the shallow marine sandstones of the Jurassic Brent Group, which is overlain by Upper Jurassic marine shales of the Viking Group. The depth to the top reservoir is 3885 mMSL, and the sediments are highly
(a) 0
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overpressured as the pore pressures reach 76 MPa (1.97 g cm 3; 0.85 psi ft^1) both in the reservoir and in the Viking Group cap rock. The average Plio/Pleistocene burial rate has been about120 m Myr^1, because approximately 600 m of sediments were deposited during the 5 Myr Plio Pleistocene time span (Fig. 11). The pore pressure starts to deviate from hydrostatic pressure at around 3000 m in this well, and it increases very steadily from 3500 m and down to the top reservoir at 3885 m (Fig.11a).We consider this 385-m interval as the top seal for this structure. The overpressure gradient across this seal is then calculated from Eqn. (6), giving an overpressure gradient of 44 MPa km 1. The Darcy £uid £ow velocity vs. depth for this well was calculated by the software BasinMod 1Dt (June 2003 release), giving a present day £uid velocity of 3 m Myr^1 at 3885-m depth (Fig. 11b). The input parameters for this modelling are those given by Nordgrd Bols etal. (2004), and were designed to simulate e¡ective stress-driven compaction at shallow burial depth and temperature-driven, stress-insensitive compaction at greater burial. The modelled thickness of the deepest layers were however increased by 2 km to ensure that the water £ux from underlying sediments was not underestimated. A rapidly subsiding reservoir in the Eugene Island area o¡shore Gulf of Mexico was selected as case 2.The Eugene
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Northern North Sea: Well 34/10-35 Measured reservoir depth: Reservoir depth subseafloor: Reservoir pressure: Overpressure gradient: Present day burial rate:
3885 m MSL 3750 m 76 MPa 44 MPa /km 120 m / My
(Cenomanian-Coniacian) Lower Cretaceous Upper Jurassic
Middle Jurassic and older
6000
7000 0 10 20 30 40 50 Fluid velocity (m/My)
Fig. 11. (a) Pore pressure vs. depth relationship (adapted from Nordgrd Bols et al., 2004), and (b) modelled £uid velocity vs. depth for the North Sea Well 34/10-35.The formation £uid pressure illustrated by the solid line is mainly derived from increased mud gas content, including trip gas through the shaly units down to top Jurassic.The reservoir pressure gradient is con¢rmed by repeat formation tests to be 1.97 g cm 3, which equals around 76 MPa at the top reservoir depth (shown by the star symbol). r 2005 Blackwell Publishing Ltd, Basin Research, 17, 583^599
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20 1719
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6000 Gulf of Mexico: Well 330 B-13, Eugene Island 1900 m MSL Measured reservoir depth: 1820 m Reservoir depth subseafloor: 30 MPa Reservoir pressure: 15 MPa/km Overpressure gradient: Up to 2.4 km/My Present day burial rate:
Chronostratigraphy
80
10
Age (My)
0
7000
8000 0 100 200 300 400 Fluid velocity (m / My)
Fig. 12. (a) Pore pressure vs. depth relationship (adapted from Gordon & Flemings, 1998), and (b) modelled £uid velocity vs. depth for the Eugene Island block 330, Gulf of Mexico.The pore pressure illustrated by a solid line in (a) is predicted from drilling mud density, and the stars show direct measurements of pore pressure in individual sandy units.
Island South Addition Block 330 is a salt withdrawal minibasin located on the continental shelf o¡shore Louisiana. The basin sediments comprise a Pliocene prodelta unit, a Pleistocene proximal deltaic unit and a younger £uvial unit. Hydrocarbons, both oil and gas, are accumulated in both fault-dependent traps and independent clo sures, and there are several sandy reservoir units through the whole sequence which are all sealed by clay-dominated lithologies. The sedimentation rate in this basin is extremely rapid, and has varied between 2.0 and 2.4 km Myr 1 over the past 2.2 Myr (Gordon & Flemings, 1998). This subsidence rate is approximately 20 times faster than the Plio -Pleistocene subsidence in the Northern North Sea. The Eugene Island Basin is highly overpressured in the deeper sections (Fig. 12). One of the shallow overpressured reservoir units in Well 330 B-13 is part of the Pleistocene proximal deltaic unit, and the top of this reservoir may broadly be represented by the chrono - stratigraphical surface H. sellii (1.27 Myr) (Gordon & Flemings, 1998).We focus our investigations on this reservoir level, as such shallow reservoir units generally have higher £uid velocities than more deeply buried units, and because the overpressure gradient in this area increases with depth. By selecting the reservoir unit at the H. sellii level, we have therefore not selected
594
the most favourable cap rock with respect to seal capacity among the overpressured cap rocks in this well. The overpressure gradient for the cap rock above the H. sellii unit was calculated to be 15 MPa km 1 (Fig. 12a) by the use of Eqn. (6). The Darcy £uid velocity calculations were performed by the same procedure as that of the North Sea example, which included simulation of e¡ective stress-driven compaction at shallow burial depth and thermally driven, stress-insensitive compaction at greater burial. The parameters in the equations that simulate compaction were adjusted to match the £uid pressures in this well. The calculated Darcy velocities for the Eugene Island area are shown in Fig. 12b. The present day £uid velocity at 1900 m burial depth in case 2 is modelled to be 120 m Myr 1, a velocity that is 40 times faster than the modelled £uid velocity in case 1. Table 2 lists the input parameters for the two case studies.The critical pore throats were computed from permeabilities based on the regression line through all available pore throat/permeability data (Eqn. 13). The water viscosities, oil densities and interfacial tensions were taken from Figs 2, 8 and 9, respectively, using temperature gradients of 35 1C km 1 for the North Sea (Fraser et al., 2002) and 22 1C km 1 for Eugene Island (Losh et al., 1999). For simr 2005 Blackwell Publishing Ltd, Basin Research, 17, 583^599
1311 2413 182 369
plicity, surface temperatures at sea £oor were set to 7 1C in both cases. The calculated minimum seal capacities for these cases are about 1.3 km (gas column) and 2.4 km (oil column) for case1, and about180 m (gas column) and 370 m (oil column) for case 2 (Table 2). These values suggest that observed overpressure gradients of comparable magnitude to those in our case studies are indicative of su⁄cient seal capacities in most geological settings, as even the least favourable case 2 indicates top seal capacities close to 200 m for gas. However, smaller hydrocarbon columns exist in both areas because trap elements other than the cap rock capacity (like structural spill or fracturing/reactivated faults) often limit hydrocarbon columns. In the following, we analyse the sensitivity of these results with emphasis on the parameter ranges that may invalidate positive conclusions regarding the cap rock seal capacity. Permeabilities were computed from Eqn. (7), critical pore throat diameters were computed from Eqn. (13) and seal capacities were calculated from Eqn. (14).
35 38 56 29 0.22 0.54 0.14 0.78 14 14 146 146 6.5 10 7 6.5 10 7 1.5 10 4 1.5 10 4 0.3 0.3 0.6 0.6 Case 1 (North Sea) ^ gas Case 1 (N. Sea) ^ oil Case 2 (GOM) ^ gas Case 2 (GOM) ^ oil
3750 3750 1820 1820
138 138 47 47
44 44 15 15
3 3 120 120
Hydrocarbon density (g cm 3) Pore throat diameter (nm) Water viscosity (cp) Temperature ( 1C) Depth (m)
Table 2. Input parameters for the two case studies
Overpressure gradient (MPa km 1)
Darcy velocity (m Myr 1)
Computed permeability (mD)
Interfacial tension (mN m 1)
Seal capacity (m)
Seal capacity estimation
r 2005 Blackwell Publishing Ltd, Basin Research, 17, 583^599
Sensitivity analyses of input parameters and the permeability/pore throat relationship The seal capacities are in£uenced by water viscosity, hydrocarbon density, interfacial tension, overpressure gradient in the cap rock and vertical Darcy velocity (Table 2). The calculated seal capacities are also heavily dependent on the relationship between permeability and pore throat diameters (Figs 5 and 7). Figure 13 summarizes how variations in the input parameters in£uence the calculated seal capacity.The ranges for the input parameters were selected to ensure that most values that would occur in the evaluation of an exploration prospect are represented. For simplicity, we assess the seal capacity of gas in both cases 1 and 2, as the seal capacity of oil will exceed the seal capacity for gas in most cases. Water viscosity, hydrocarbon density and interfacial tension As is clear from Fig.13a^c, case1is generally more sensitive to changes in input parameters than case 2. However, the seal capacity for case 1 is never reduced to below 750 m, regardless of the choice of input parameters.The seal capacity for case 2 also stays fairly stable (close to 200 m) for a wide range in the input parameter, but there is a considerable high-side potential to the seal capacity if the hydrocarbon density increases. For the gas-type £uid in case 2, the seal capacity is reduced to below100 m only when the interfacial tension is lower than about 40 mN m 1. Note that hydrocarbon density and interfacial tension are correlated variables, as hydrocarbon density is one of the critical factors in£uencing the interfacial tension (Eqns (15) and (17)). However, in our sensitivity analyses, we treat these two variables as independent parameters, such that uncertainties in the applied relationship between density and interfacial tension (Eqns (15) and (17)) are also addressed. Overpressure gradient Overpressure gradients of 0 MPa km 1 give zero calculated seal capacity by the use of our suggested method
595
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Most likely parameter, Case 1 Most likely parameter, Case 2
Case 1, all data Case 2, all data Artefact, Case 1
Case 1, Yang & Aplin data Case 2, Yang & Aplin data Artefact, Case 2
Fig. 13. Sensitivity of calculated seal capacity to variations in (a) water viscosity, (b) hydrocarbon density, (c) interfacial tension between water and hydrocarbons, (d) pressure gradient in the cap rock, (e) vertical water (Darcy) velocity and (f) vertical water (Darcy) velocity calculated from the data from Yang & Aplin (submitted) and all data combined.The crosses and circles represent the calculated parameter values from the case studies, the blue crosses showing case 1 and the red circles case 2.
(Fig.13d).This result is however an artefact of the method, as the method cannot be used for seals characterized by hydrostatic pressure gradients. Such seals may have signi¢cant seal capacities as well. Furthermore, an overpressure gradient as low as 2 MPa km 1, which is approximately the lowest value that can be identi¢ed
596
visually from pore pressure vs. depth plots as those of Figs 11a and 12a, still results in calculated seal capacities of around 350 m for case 1 and 75 m for case 2. This means that even if the sensitivity plot (Fig. 13d) shows some sensitivity of this parameter, signi¢cant seal capacities remain as long as there exists a measurable r 2005 Blackwell Publishing Ltd, Basin Research, 17, 583^599
Seal capacity estimation Table 3. In£uence on computed seal capacity from di¡erent permeability vs. pore throat relationships for the two case studies Case 1: North Sea
Case 2: Gulf of Mexico
Kvs. pore throat relationship
Gas seal capacity (m)
Oil seal capacity (m)
Gas seal capacity (m)
Oil seal capacity (m)
Yang & Aplin (submitted) Schl˛mer & Kroos (1997) Katsube et al. (1998) All data compiled
1386 1446 1481 1311
2552 2663 2726 2413
40 390 563 182
81 789 1140 369
overpressure gradient through the seal in our two case studies. Vertical £uid velocity The vertical £uid velocity in£uences the calculated seal capacity signi¢cantly (Fig. 13e). Not only is the calculated seal capacity drastically reduced as the vertical Darcy velo city increases, but the sensitivity curves for the two cases nearly overlap. This observation demonstrates that the effects of the other input parameters for the two cases are of comparatively less importance. However, the sensitivity to £uid velocity drives the seal capacity estimates towards very high values for low £uid velocities.The fact that an increase in £uid velocity causes a reduction in the calculated seal capacity still causes the calculated seal capacity for gas in case 2 to be in excess of 400 m as long as the Darcy velo city is slower than 20 m Myr 1, and in excess of 100 m when the Darcy velocity is as high as 200 m Myr 1. Permeability/pore throat relationship The calculated in£uence of vertical £uid velocity also depends on the applied relationship between cap rock permeability and the critical pore throat diameter. The dependencies of these relationships on the calculated seal capacities of the case studies are listed in Table 3. As the data presented by Yang & Aplin (submitted) give the most negative seal capacity predictions, we display calculations of seal capacities based on these data together with those based on all available data separately (Fig. 13f). This ¢gure demonstrates that even if the seal capacity estimates are reduced when applying the relationship based on the data from Yang & Aplin (submitted) (Eqn. (10)) instead of the relationship derived from all available data (Eqn. (13)), the calculated seal capacities based on the least favourable relationship (Eqn. (10)) are still larger than 250 m for gas in case 2 and in excess of 600 m for gas in case 1 for Darcy velocities of 10 m Myr 1 or less.The seal capacity for case 2 is still more than 100 m for Darcy velocities 40 m Myr 1. For oil, the calculated seal capacities will be even larger.
increases. This may happen if the capillary pressure at the top of a hydrocarbon column is in£uenced by other factors than pore £uid density contrasts and hydrocarbon column heights. Teige et al. (in press) demonstrated by laboratory experiments that the overpressure in the water phase near the top of an oil- saturated reservoir may be reduced compared with the overpressure in the aquifer below the reservoir in some circumstances (their Fig. 1). This will happen if an increase in the oil phase pressure, as a response to a large oil column, reduces the diameter of the wetting phase water £ow path in the acute corners of the pore space. This e¡ect will lead to a reduced permeability of the wetting phase water.The e¡ect is however insigni¢cant in most cases, but may be of importance in reservoir rocks with very low permeabilities and where large columns of low-density hydrocarbons are present. If the reduced permeability of the wetting phase water is signi¢cant enough to slow down the water £ux through the reservoir, it will result in lower water overpressure and a related increase in the capillary pressure at the top of the reservoir. Hence, a reduction in the seal capacity can occur in some geological settings. According to calculations performed by Teige et al. (in press), a relatively high vertical £uid velocity of15 m Myr 1 (¢ve times the vertical £uid velocity in the North Sea) is needed to cause a capillary pressure increase of 0.6 MPa for an oil column (oil density 5 0.6 g cm 3) of 250 m in a reservoir with a permeability of 10 mD and a porosity of 17%.The total capillary pressure at the top of such a reservoir would be 1 MPa, assuming a virtually constant water overpressure through the reservoir. The total capillary pressure at the top reservoir is hence increased to 1.6 MPa when the reduced residual water permeability and a vertical £uid £ux is accounted for.This increase in the capillary pressure will reduce the seal capacity of the overlying cap rock from 400 to 250 m. For comparison, the presence of a similar 75 m oil column in a high-quality reservoir (35% porosity, 1 D permeability) will only increase the capillary pressure with about .0018 MPa and cause no reduction in the oil column height.
Changes in capillary pressures and impact on seal capacity
SUMMARY AND CONCLUSIONS
The seal capacity related to a speci¢c cap rock will be reduced if the capillary pressure at the top of the reservoir
Overpressures are indicative of small pore throats in the seals that delineate pressure compartments.We have used
r 2005 Blackwell Publishing Ltd, Basin Research, 17, 583^599
597
H. M. Nordgrd Bols et al. the occurrence of formation overpressures to estimate top seal capacity, by calculating (in sequence) £uid velocity, top seal permeability, critical pore throat diameter of the seal and the possible hydrocarbon column heights that can be trapped by such seals. The estimates based on our threestep method are assumed to represent conservative values of the seal capacity because all £uid £ow was assumed to be vertical. In reality, some £uid £ow is lateral from the basin centre towards the £anks, which implies that we have overestimated the vertical £uid £ow and hence underestimated the seal capacity. In spite of our presumed too low estimates of seal capacities, our results suggest that observations of overpressure gradients across a seal are indicative of a signi¢cant membrane seal capacity in most cases, provided that the seal is water wet. This conclusion appears to be valid for most burial histories, but sealing of large hydrocarbon columns in areas with rapid sediment compaction, such as in depocentres of modern delta systems, cannot be inferred from observations of subsurface overpressures alone.
ACKNOWLEDGEMENTS This work was performed as a Statoil research activity, and Statoil is gratefully acknowledged for the permission to publish the results.We also thank Dave Dewhurst for constructive critisicm to an earlier version of the manuscript, and for converting the Firoozabadi & Ramey (1998) interfacial tension data into temperature- and density-dependent relationships. Elin Storsten is thanked for graphical support.
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Manuscript received 12 February 2005; Manuscript accepted 31 October 2005.
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