Pressure prediction in the Bullwinkle Basin through petrophysics and flow modeling (Green Canyon 65, Gulf of Mexico)

Transcription

1 Marine and Petroleum Geology 21 (2004) Pressure prediction in the Bullwinkle Basin through petrophysics and flow modeling (Green Canyon 65, Gulf of Mexico) P.B. Flemings a, *, J.A. Lupa b a Pennsylvania State University, Department of Geosciences, 442 Deike Building, University Park, PA 16802, USA b ConocoPhillips, Conoco Center, 600 N Dairy Ashford, Houston, TX 77079, USA Received 14 April 2002; received in revised form 7 July 2004; accepted 10 September 2004 Abstract Reservoir pressures within the Bullwinkle minibasin (Green Canyon 65, Gulf of Mexico continental slope) increase at a hydrostatic gradient whereas pressures predicted from porosity within mudstones bounding these reservoirs increase at a lithostatic gradient: they are equal at a depth 1/3 of the way down from the crest of the structure. Two- and three-dimensional steady-state flow models demonstrate that bowl-shaped structures will have lower pressures than equivalent two-dimensional structures and that if a low permeability salt layer underlies the basin, the pressure is reduced. We conclude that at Bullwinkle, pressure is reduced due to an underlying salt body and the bowl-shape of the basin. A geometric approach to predict sandstone pressure is to assume that the reservoir pressure equals the area-weighted average of the mudstone pressure. When the mudstone pressure gradient is constant, as at Bullwinkle, the reservoir pressure equals the mudstone pressure at the average depth (centroid) of the reservoir. q 2004 Elsevier Ltd. All rights reserved. Keywords: Overpressure; Fluid flow; Centroid; Pressure prediction 1. Introduction Overpressure in sedimentary basins drives fluid flow, impacts the state of stress, and affects hydrocarbon migration and entrapment. It is often predicted from the consolidation state of mudstones. However, to predict reservoir pore pressure, the relationship between mudstone pressure and reservoir pressure must be understood (Darby, Haszeldine, & Couples, 1998; Dugan & Flemings, 2000; Flemings, Stump, Finkbeiner, & Zoback, 2002; Saffer, Silver, Fisher, Tobin, & Moran, 2000; Yardley & Swarbrick, 2000). We study the Bullwinkle (Green Canyon 65) salt withdrawal minibasin in the Gulf of Mexico (Fig. 1). We first characterize overpressure in the sandstone and in the mudstone across the basin using in situ measurements and a porosity-effective stress model. We then develop * Corresponding author. Tel.: C ; fax: C addresses: flemings@geosc.psu.edu (P.B. Flemings), j.lupa@ conocophillips.com (J.A. Lupa). 2- and 3-D, steady-state flow models that examine how reservoir geometry and the presence of salt affect reservoir pressure. Based on modeling and observation, we propose an empirical geometric approach to predict sandstone pressure from bounding mudstone pressure. We suggest that the abnormally low pressures in the Bullwinkle sandstone results from the presence of a low permeability salt beneath the Bullwinkle minibasin. 2. The Bullwinkle Basin and the J sandstone package 2.1. Geology of the Bullwinkle Basin The Bullwinkle mini basin lies 250 km southwest of New Orleans, Louisiana, USA (Fig. 1). The Bullwinkle oil field is on its eastern side, and the Rocky gas field is on its western side. Salt ridges bound the basin to the west and southeast and a salt diapir is present to the northeast (Fig. 2). To the northwest, the basin is bounded by a normal fault that soles into the edge of salt and into the top of an evacuated salt /$ - see front matter q 2004 Elsevier Ltd. All rights reserved. doi: /j.marpetgeo

2 1312 P.B. Flemings, J.A. Lupa / Marine and Petroleum Geology 21 (2004) Nomenclature b mudstone compressibility (M K1 LT 2 ) Dt formation sonic travel-time (TL K1 ) Dt ma matrix sonic travel-time (TL K1 ) f porosity f 0 reference porosity m viscosity (ML K1 T K1 ) r w water density (ML K3 ) r o oil density (ML K3 ) r g gas density (ML K3 ) sv 0 vertical effective stress (ML K1 T K2 ) s v overburden stress (ML K1 T K2 ) f acoustic formation factor g acceleration of gravity (LT K2 ) k permeability (L 2 ) k permeability (L 2 ) P ms mudstone overpressure (ML K1 T K2 ) P ms mudstone pressure (ML K1 T K2 ) P w reservoir water phase pressure (ML K1 T K2 ) P o oil phase pressure (ML K1 T K2 ) P g gas phase pressure (ML K1 T K2 ) P w reservoir water phase overpressure (ML K1 T K2 ) r radius (L) r w water density (ML K3 ) r o oil density (ML K3 ) r g gas density (ML K3 ) z depth beneath sea surface (L) z centroid depth (L) Z dimensionless depth where P w ZP ms ( ) ramp. The basin is floored by salt in some areas and by a salt weld (evacuated salt) in other areas. It is bowl-shaped and has up to 700 m of structural relief (Fig. 2). Prior to the formation of the Bullwinkle Basin, allocthonous salt tongues encroached from the north, southeast and west, and sutured near the seafloor (Rowan, Jackson, & Trudgill, 1999). The minibasin formed in the Late Miocene-Early Pliocene by sediment loading and gravitational collapse of this salt. Deposition rates were less than 1 km/ma prior to 3 Ma and increased to almost 4 km/ Ma from 1 Ma to present (Fig. 3). Rapid Late Pliocene sedimentation was coeval with a second order sea level fall and the capture of a large drainage area by the Mississippi River in the Pleistocene (Prather, Booth, Steffens, & Craig, 1998). During this time, the Bullwinkle Basin was just west of the Mississippi delta depocenter (Ostermeier et al., 2000) Geology of the J sandstone package The 3.35 Ma J sandstone package is bowl-shaped and has a diameter of 5 km (Fig. 2). Its five sandstones (J0, J1, J2, J3, J4) are not continuous across the basin; however, the J2 and J0 together cover the extent of the basin (Fig. 2c). The sandstones pinch out against salt to the south, east and west, and into mudstone to the north (Fig. 2). The J sandstone package hosts the majority of the hydrocarbon reserves. It is composed of interconnected channel and sheet turbidite sandstones that are interbedded with debris flows and mudstones; it is overlain by 150 m of bathyal mudstones. The depositional architecture transitions upward from ponded, internally amalgamated, sandstones to channelized sandstones, which indicates increasing depositional energy higher in the section (Holman & Robertson, 1994). The top of the J sandstone section has multiple erosional unconformities, suggesting a period of sediment bypass. Pressure drawdown at each well followed the same depletion curve during production (Holman & Robertson, 1994; Kikani & Smith, 1996), indicating that all the sandstones are in pressure communication. 3. Pressure characterization 3.1. Sandstone pressure Repeat formation tester (RFT) pressure measurements were taken prior to production in three wells (Table 1, Fig. 4). We assumed that within the sandstones, fluid pressures follow their respective static pressure gradients: thus the water phase pressure in the reservoir is described with a single overpressure (P w *) P w Z P w Kr w gz; (1) Fig. 1. The Bullwinkle Minibasin is located in 400 m of water depth on the slope of the Gulf of Mexico. Bathymetric contours are in meters (C.I.Z 500 m).

3 P.B. Flemings, J.A. Lupa / Marine and Petroleum Geology 21 (2004) Fig. 2. (a) Cross-section of the Bullwinkle Basin (located in (b)). Thick vertical black lines record the and 64-1-BP well paths. Thin black lines are faults. Salt welds are represented by two black dots. (b) Structure map of the top of salt (dark gray) determined from 3D seismic. Contours are in meters beneath the sea surface. The extent of the J2 and J0 sandstones are shaded light gray. Heavy gray long-dashed lines indicate the edge of salt beneath the J sandstones. Light short-dashed lines are the top of salt structure contours where salt underlies the J sandstone. The top of salt is only 100 m beneath the J sandstone at the well. (c) Structure map of the J2 and J0 sandstones in meters beneath the sea surface. where P w is fluid pressure, r w is water density, g the acceleration of gravity and z is depth in TVDSS. P w ranges from 80% to over 93% of the overburden (s v ) at Bullwinkle (Table 1)(Fig. 4). Within the minibasin, the J through H sandstones all have approximately the same overpressure. Two sandstones outside the basin, the I Boxer and the J Boxer, have markedly higher overpressure than sandstones at equivalent depth within the basin (Figs. 2a and 4) for mudstones (Issler, 1992; Stump and Flemings, 2002). The gamma ray (GR) log was used to filter the wireline log so that only mudstone porosity was calculated. The relationship between porosity (f) and vertical effective stress ðs 0 vþ was calculated with the empirical 3.2. Mudstone pressure prediction Mudstone has low permeability, and routine measurement of pore pressure is not possible. Instead, we estimated mudstone pressure from porosity. Porosity was calculated from sonic log data (Fig. 5) using a relationship developed by Issler (1992): f Z 1 K Dt ð1=f Þ ma : (2) Dt Dt ma is the matrix travel-time, Dt is the sonic travel-time, and f is the acoustic formation factor. We assume f to be Fig. 3. Pleistocene sedimentation rates in the Bullwinkle Basin reached 4 km/ma. Rates are estimated by recalculating the stratigraphic thickness at the time of deposition assuming a surface porosity of 60% (a 1 km interval of sediment deposited over 1 Ma with a 30% porosity today had a sedimentation ratez(1 km/1 Ma)!(0.6/0.3)Z2 km/ma). The biostratigraphic correlation is from Styzen (1996): 1ZPM 4; 2ZPM1R; 3ZNPM 0; 4ZNP 3.3; 5ZNP 3; 6ZNP 2.9; 7ZNP1.78; 8ZNP 1.68; 9ZNP 1.55.

4 1314 P.B. Flemings, J.A. Lupa / Marine and Petroleum Geology 21 (2004) Table 1 Pressure measurements Sandstone Well RFT (MPa) Depth (m) Fluid phase P w (MPa) P w (MPa) s v (MPa) f ms F Gas G Water G Water I3A Water I Oil J Oil J Oil J Oil J Oil J Water J Water J ST Oil J ST Gas I BP Gas J Boxer 64-1-BP Gas relationship f Z f 0 e Kbs0 v ; (3) where f 0 is the reference porosity and b is the mudstone compressibility (Hart, Flemings, & Deshpande, 1995; Rubey & Hubbert, 1959). Vertical effective stress is s 0 v Z s v KP ms ; (4) where s v is the overburden stress and P ms is the mudstone pressure. s v is calculated by integrating logging-based bulk density measurements. We used two approaches to constrain b and f 0. In the first approach, we assumed that between the onset of logging at 300 m below the seafloor (mbsf) and 920 mbsf, pore pressures are hydrostatic (grey zone, Fig. 5). The vertical effective stress ðs 0 vþ in this zone was calculated given this assumed pressure. A least squares regression of log f vs ðs 0 vþ yielded a compressibility (b of 3.62!10 K2 MPa K1 and reference porosity (f 0 ) of 40% (Fig. 6). In the second approach, the effective stress for the mudstone bounding the sandstone is calculated from Eq. (4), and P ms is assumed to equal the reservoir water pressure (P w )(Fig. 6). Mudstone porosity is estimated by projecting the calculated mudstone porosity to the sandstone mudstone interface (Fig. 7). b and f 0 are found to equal 3.92! 10 K2 MPa K1, and 37.5%, respectively (Fig. 6). Not surprisingly, the two approaches yield different porosity-effective stress relationships (Fig. 6). For example, the deepest sample in the shallow section (where we assumed hydrostatic pressures) has an effective stress of almost 8 MPa and a porosity of 32% (Fig. 6, black diamonds). The deeper (3360 mbsf) J Boxer sandstone has the same effective stress but the porosity of the mudstone is only 27% (Fig. 6, circle). This either means that the b and/or f 0 determined in the shallow section does not apply for the deeper sediments (cf., Hart et al., 1995) or that the shallow zone (0 920 mbsf) is overpressured. Mudstone pressure is calculated by rearranging Eq. (3): P ms Z s v K 1 ln f 0 : (5) b f In the approach constrained by the reservoir pressures, predicted overpressures near the sea floor reach 2.5 MPa at just 600 mbsf (Fig. 8a). These pressures are approximately equal to the pressures generated by the mudweights used during drilling (Fig. 8a). At depth, the same approach predicts mudstone pressures that approximately equal the reservoir pressures (Fig. 8b). This latter result is not surprising since it was assumed that the mudstone pressure equaled the reservoir pressure to constrain the porosityeffective stress model. In contrast, mudstone pressures predicted from the assumption that the shallow section is hydrostatically pressured are less than the reservoir pressures Fig. 4. In situ pressures of Bullwinkle reservoirs. Pressures (black dots) were obtained from Repeat Formation Test measurements (RFTs). Water, oil and gas phase (P w (black), P o (grey), P g (dotted)) pressures were calculated assuming r w Z1050 kg/m 3, r o Z720 kg/m 3, r g Z230 kg/m 3, knowledge of fluid contacts from seismic, and a hydrostatic gradient. The J Boxer and I Boxer sandstones are west of the basin (Fig. 2).

5 P.B. Flemings, J.A. Lupa / Marine and Petroleum Geology 21 (2004) Fig. 5. Sonic slowness (DT) (left) and mudstone porosity (right) calculated from DT log and Eq. (2) for the well (located in Fig. 2). The gray area shows the region that could be interpreted as hydrostatically pressured (see text). (Fig. 8b, dash-dot line). For example, P ms is w4 MPa less than the reservoir pressure in the F sandstone (Fig. 8b). The simplest explanation for the difference in pressures predicted from the two approaches is that the shallow section is overpressured, not hydrostatically pressured. This is common where sedimentation rates were high Fig. 7. Mudstone overpressure at (a) the A-3-BP well (near the crest of the reservoir); (b) the A-1 well; and (c) the A-4-BP (in the syncline). When the sonic log does not extend to the sandstone top, mudstone overpressure is projected to the sandstone top (dashed line). The projected mudstone overpressures are used in Fig. 9. Measured water (square) and oil (circle) overpressures for the sandstone are indicated at the sandstone-mudstone boundary. The gamma ray log (GR), sonic log (DT) and calculated mudstone porosity are shown for reference. Fig. 6. Mudstone porosity (f) vs vertical effective stress ðs 0 vþ. fks 0 v relationship is determined in two ways: (1) shallow Hydrostatic assumption (black diamonds) between 300 and 920 mbsf the mudstone porosity is calculated from the sonic log in the well (shaded zone, Fig. 5) and cross-plotted against the hydrostatic effective stress; and (2) porosity is calculated from the sonic log in the vicinity of each reservoir sandstone and cross-plotted against the vertical effective stress (s v KP w ) for that location (gray circles). The error bars represent water phase vertical effective stress at the structural crest and the low point of each sandstone. (Dugan & Flemings, 2000; Ostermeier et al., 2000) and the Pleistocene sedimentation rate was extraordinarily high at Bullwinkle (4 km/m.y., Fig. 3). At Mississippi Canyon 810 (300 km from GC 65), a region with a similar Pleistocene to Recent depositional history, Ostermeier et al. (2000) measured overpressures that reach 2.75 MPa at 600 mbsf (PZw0.8s v ). Modeling also predicts that deposition rates of 4 km/ma of low permeability clay and silt will generate significant overpressure (Dugan & Flemings, 2000; Gibson, 1958; Gordon & Flemings, 1998). Thus, we interpret that sediments near the sea floor are overpressured and we will further analyze only the pressure predictions that are constrained by the reservoir pressures Pressure in the J sandstone package We illustrate the variation in porosity and pressure near the J sandstone package in three wells (Fig. 7). Mudstone

6 1316 P.B. Flemings, J.A. Lupa / Marine and Petroleum Geology 21 (2004) Fig. 8. (a) Predicted pressure (dotted line) in the shallow section of the well when the pressure prediction is calibrated to the reservoir pressures. The borehole pressure caused by the drilling mud is shown by the solid line. (b) Predicted pressures vs water phase pressures (from RFT measurements) in the reservoir interval of the well. When the pressure prediction is calibrated by assuming the shallow section is hydrostatically pressured, (dashed line) mudstone pressures are lower than reservoir pressures. When the pressure prediction is calibrated to the reservoir pressures (dotted line), predicted mudstone pressures equal the reservoir pressures. pressure near the sandstone mudstone interface is often difficult to predict because sandstone content gradually increases as the sandstone is approached: thus clean mudstones are not sampled and pressure is not predicted. To estimate the mudstone overpressure ðp msþ at the sandstone mudstone interface we linearly extrapolate the calculated P ms to the sandstone top (Fig. 7, dashed lines). Near the top of structure (wells A-3-BP, 110-SOI1, A-1), P ms increases linearly into the sandstone, yet is lower than sandstone pressure at the sandstone-mudstone interface (e.g. Fig. 7a). At the bottom of structure, the opposite behavior is observed: P ms is greater than the reservoir pressure at the sandstone mudstone interface (e.g. Fig. 7c). In the wells that penetrate the J sandstone in the deeper locations, there is a 200 m zone where the porosity and predicted pressure decrease toward the J sandstone (wells A-4-BP, A-5-BP, GC-65-1 and GC-65-1-ST) (Fig. 7c). One striking result is that mudstone porosity is approximately constant above the J sandstone, although its depth changes by w500 m. For this to be the case, the effective stress must be constant (Eq. (3)) and therefore the predicted mudstone pressure follows the lithostatic gradient (Eq. (5)) as shown in Fig. 9. While the predicted mudstone pressure follows the lithostatic gradient, the water pressure in the reservoir follows the hydrostatic gradient (vertical line, Fig. 9). As a result, any well that penetrates the J sandstone above km has a mudstone pressure that is less than the reservoir pressure, whereas any well that penetrates beneath this point has a mudstone pressure that is greater than the reservoir pressure (Fig. 9). Wells that overlie the salt tend to fall below the trend (e.g. wells A-36, 109-2). Flemings et al. (2002) introduced the parameter Z, the dimensionless depth along structure where the sandstone and mudstone pressure are equal. It is calculated by dividing the vertical distance from the crest to where the sandstone and mudstone pressures are equal by the total relief of the sandstone. In this example, ZZw1/3: the sandstone pressure equals the mudstone pressure 1/3 of the way down the structure. Above Z, the sandstone pressure exceeds the mudstone pressure; below Z, the sandstone pressure is less than the mudstone pressure (Table 2). The mudstone overpressure mimics the basin geometry: at equivalent depths, P ms is higher at the margins than the center (Fig. 10). In addition, the P ms gradient at the margins (10.5 MPa/km) is greater than at the basin center (7.0 MPa/km). In the one well that penetrated significantly Fig. 9. Predicted overpressure ðp msþ in mudstones immediately above the J sandstone (black diamonds) and water phase overpressure ðp wþ of the J sandstones. The P ms gradient (slope of b b 0 ) is 9.6 MPa/km. The 110- SOI-1, and A-36 wells overlie salt (Fig. 2). The overpressure trends a a 0 and b b 0 are shown in Fig. 15.

7 P.B. Flemings, J.A. Lupa / Marine and Petroleum Geology 21 (2004) Table 2 Sandstone characteristics Sandstone Top (m) beneath the J sandstone (109-1), P ms rises very rapidly beneath the J sandstone (w20 MPa/km). 4. Flow modeling 4.1. Modeling approach Bottom (m) OWC (m) GOC (m) GWC (m) F G G I3A I J J J I J Boxer We use flow modeling to gain insight into the pressure distribution at Bullwinkle. Today, the Bullwinkle Basin is dissipating pressures generated by rapid sediment loading in the past. LaPlace s equation, ðk=mþv 2 P w Z 0; (6) is used to visualize flow during this dissipation, where k is the instrinsic permeability and m is the dynamic viscosity. Eq. (6) describes a steady-state dynamic flow process and is particularly useful for understanding how strong permeability contrasts (such as those between reservoirs, mudstone, and salt) control the flow field and pressure distribution. It is applicable as long as there is little ongoing sediment loading and the vertical relief of the sandstone bodies is small relative to the thickness of the basin (Flemings et al., 2002). This approach represents a middle ground between static models (Flemings et al., 2002) that do not consider flow and time-dependant simulations (Dugan & Flemings, 2000; Yardley & Swarbrick, 2000). We solved Eq. (6) numerically in 2- (Cartesian coordinates) and 3-D (cylindrical coordinates) (Fig. 11). Constant fluid density and constant viscosity were assumed. A full derivation of the finite difference approximations is found in Lupa (2002). For all models, overpressure at the top (3020 m depth) and bottom (4670 m depth) is assumed to equal and MPa, respectively; this resulted in an overpressure gradient far from the sandstone of 9.6 MPa/km. This is the same, approximately lithostatic, gradient observed in the Bullwinkle petrophysical analysis (Fig. 9). We refer to this as the far field mudstone pressure gradient. Far from the sandstone, no flow is assumed in the lateral directions. A layer-parallel mudstone permeability of 1!10 K21 m 2 and layer-perpendicular mudstone permeability of 1!10 K19 m 2 are assumed (Neuzil, 1994; Stump, 1998). The sandstone and salt permeability are assumed to be isotropic and equal to 1!10 K12, and 1!10 K23 m 2, respectively (Best, 2002). More complicated mudstone porosity and permeability relationships could be assumed. However, the Bullwinkle mudstones near the J sandstone all have approximately the same porosity; thus there is not a significant variation in the mudstone permeability. Furthermore, modeling shows that the very large contrast between sandstone and mudstone permeability drives the model; smaller scale variation in mudstone permeability will not have a significant effect. We examine how the 3-D geometry of the basin affects flow relative to a 2-D model and we explore the effect of a low permeability salt layer through three models: (1) a 2-D V- shaped sandstone (2-D Model), (2) a 3-D cone-shaped sandstone (3-D Model) and (3) a 3-D cone-shaped sandstone with an underlying salt body (3-D Salt Model) (Fig. 11). In the model, the synclinal lowpoint of the sandstone is at 3640 m depth and its crest is at 4050 m. The crestal position Fig. 10. Overpressure cross-section through the Bullwinkle field (located in Fig. 2). Well bores are indicated by vertical black lines. The overpressure contours are pressures predicted from mudstone that are extrapolated from well to well. Sandstone overpressure ðp wþ is from RFT measurements. Salt bodies are shown with dashed lines, with salt welds indicated by black dots.

8 1318 P.B. Flemings, J.A. Lupa / Marine and Petroleum Geology 21 (2004) is the average depth of the top of the J sandstone: the tops of some J sandstone members are higher, but the sandstones are not continuous around the basin at shallower depths (Fig. 2c) Modeling results Fig. 11. The bowl-shaped basin is modeled in 2-D as a V shape (2-D Model) and in 3-D as a cone (3-D Model). In addition, one of the simulations assumes a salt layer underlies the cone (3-D Salt Model). Because of symmetry, no flow occurs across the center of the basin. Thus, the model domain needs to In the 2-D Model, overpressure contours are depressed and closely spaced in the syncline beneath the sandstone whereas they are elevated and compressed above the crests of the sandstone at the basin margins (Fig. 12a). Flow is focussed into the base of the syncline, whereupon it is transported laterally within the sandstone before it is expelled at the crests (streamlines, Fig. 12a). Minimal flow occurs in the mudstone above the syncline. Flow lines are not orthogonal to overpressure contours because the lateral permeability is greater than the vertical permeability. In the sandstone, pore pressure follows the hydrostatic gradient (heavy solid vertical line, Fig. 12b); thus Fig. 12. (a) Overpressure and flow in the 2-D Model. The thin dotted black lines are overpressure contours and the black lines with arrows are streamlines. Fluid flux between adjacent streamlines is constant. Where streamlines are close together, velocity is fast; where they are far apart, velocity is slow. The arrows within the sandstone (light gray) are schematic. (b) Overpressure profiles (located in Fig. 12a) through the bottom of the syncline (dashed line), and the top of the structure (dotted line). The thick vertical line is the sandstone overpressure. The far field mudstone overpressure is shown for reference (solid line).

9 P.B. Flemings, J.A. Lupa / Marine and Petroleum Geology 21 (2004) Fig. 13. Comparison of modeled overpressure for three models shown in Fig. 11. (a) 3-D Cone (grey) vs 2-D V (black). Pressure depth profiles (left) are located in the pressure cross-sections on the right. (b) 3-D Cone (grey) vs 3-D Salt Model (black). the overpressure ðp wþ is constant and equal to 21.7 MPa. In a vertical profile through the sandstone crest, P ms (dotted line) rises rapidly to equal the sandstone pressure (Fig. 12b); beneath the crest, the mudstone overpressure gradient decreases until the pressure is ultimately less than the farfield pressure. In contrast, at the structural lowpoint (dashed line, Fig. 12b), ðp msþ drops far below the far-field mudstone pressure in order to converge on the sandstone pressure. Beneath the sandstone, the pressure rises with depth toward the far-field mudstone pressure. The sandstone overpressure ðp wþ is lower in the 3-D Model (Fig. 13a, left) than in the 2-D Model (Fig. 13a, right) (21.1 vs 21.7 MPa). The mudstone pressure above the sandstone is also lower in the 3-D Model than in the 2-D Model. In the 3-D Salt Model, there is a salt layer underneath the cone-shaped sandstone body (Fig. 13b, right side). As a result of the low permeability salt layer, P w is 0.6 MPa lower than when no salt is present (20.5 vs 21.1 MPa) (Fig. 13c). In a vertical profile through the center of the basin, there is an abrupt increase in pressure with depth (w5 MPa) across the salt body (solid line, Fig. 13b) Modeling discussion The 2- and 3-D Models provide insight into how basin geometry affects reservoir pressure. The 2-D Model has a higher reservoir pressure than the 3-D Model. Because the cone expands upward, a greater fraction of its surface area is trapped in the shallower section, relative to the 2-D Model. As a result, more of the 3-D cone is exposed to the shallower, lower pressure, mudstones and its pressure is lower (Fig. 13a). All other things being equal, bowl-shaped basins will have lower pressures than equivalent 2-D synclinal geometries. Flemings et al. (2002) showed that a sandstone with constant dip encased in overpressured mudstone undergoing steady flow will have a reservoir pressure equal to the mudstone pressure at its midpoint depth. They also showed with a static loading model that with more complicated geometries (e.g. synclinal sands, domes, cones or bowls) the sandstone pressure equals the mudstone pressure at its average depth, or centroid depth (Appendix). Here, dynamic modeling of more complicated geometries also demonstrates that sandstone pressure is controlled by its geometry (e.g. the 3-D cone has lower pressure than the 2-D V ). However, in detail, the sandstone pressure is 0.5 MPa less than that predicted by the centroid depth for the 2- and 3-D Models (Fig. 14). This is due to symmetry; for all the models, the center of the basin is a no flow boundary. As a result, the mudstone at the basin center contributes less pressure and flow into the sandstone than in the case of a non-symmetric geometry. For this reason, the reservoir pressure slightly lower than is predicted from the centroid depth (Fig. 14). Where salt underlies the sandstone, there is no flow from the underlying mudstone into the sandstone (Fig. 13b). Instead, as fluids migrate upward, the low permeability salt deflects fluids laterally, and shields the sandstone from receiving flow from the underlying, overpressured mudstone (Fig. 13b). This decreases the overpressure of the bounding mudstone and reduces sandstone overpressure (Fig. 13b). 5. Discussion There are qualitative similarities between our observations in the Bullwinkle Basin and our modeling results. In both the petrophysical characterization and the modeling,

10 1320 P.B. Flemings, J.A. Lupa / Marine and Petroleum Geology 21 (2004) Fig. 14. Overpressure vs depth for the three models. The far-field gradient (thin dashed line) and the average sandstone depth (white circles) are also shown. On the right, the cumulative percentage of area is plotted against depth for the V shape vs the cone shape geometries. The 2-D V-shaped sandstone (solid line) has half of its area above the midpoint and half below, thus the average depth (50% cumulative area) is at the midpoint. The 3-D cone shaped sandstone has more area above the midpoint than below, resulting in an average depth 1/3 of the way down from top of structure. overpressure contours within the mudstone are more widely spaced in the basin center than along its flanks (Figs. 10 vs 12) and the overpressure within the permeable sandstone is constant (Figs. 9 and 12b). We infer that overpressured basins such as Bullwinkle are active hydrodynamic systems. Flow is captured into the base of these structures, focused laterally within them, and expelled at the crests (e.g. Fig. 12a). The flow rate within the sandstone is large relative to the mudstone. However, because the sandstone permeability is much larger than the mudstone permeability, it has a hydrostatic gradient The effect of salt on geopressure At a regional scale, sediments above a salt body will have lower pressures than those that are not underlain by salt (Fig. 13). This is why sandstones within the largely saltfloored Bullwinkle minibasin (I and J sandstones) have significantly lower pressures than sandstones at equivalent depths that lie outside the minibasin and are not underlain by salt (I Boxer and J Boxer) (Figs. 2 and 6). The effect of salt is also observed within the Bullwinkle minibasin. Only about half of it is underlain by salt (Fig. 2b) and wells that overlie the salt have mudstone pressures that are lower than those predicted by the regional trend (e.g. wells A-36, 109-2, Fig. 9); we infer that the pressures are lower because the underlying salt blocks any flow from below. The very abrupt pressure increase beneath the J sandstones in the well may result from flow that is focussed from the underlying salt. For example, in the 3D Salt Model, flow is focussed laterally beneath the salt layer (down the pressure gradient) and then at the upper limit of the salt, flow escapes laterally and vertically (Fig. 13b). The vertical pressure profile rises very rapidly adjacent to the tip of this salt (gray dash-dot line Fig. 13c) Predicting pressure from reservoir geometry Since the classic work of Rubey and Hubbert (1959) and Hottman and Johnson (1965), reservoir pressure has been estimated from mudstone porosity. We extend this technique to consider how reservoir geometry can be used to predict its pressure. We assume that the sandstone pressure is equal to the area-weighted average of the mudstone pressure. Given this assumption, we show (Appendix) that if the pressure gradient in the mudstone is constant, the sandstone overpressure is equal to the pressure in the mudstone at its centroid depth ðzþ, which is the center of gravity for a sandstone of constant density and thickness: Ð zda z Z A : (7) This empirical approach is compatible with modeling results presented here and elsewhere that shows that the depth distribution of the sandstone controls its pressure. We calculated the centroid depth for each J sandstone and for the entire package (Table 3, Fig. 15). In all cases, the average depth is approximately 75% of the way down from the crest of the structure (ZZ3/4) (Table 3, Fig. 15b). To estimate the reservoir pressure, we find the mudstone pressure at the centroid depth (3785 m) (open circle, Fig. 15a). The estimated pressure is 21.6, 1.95 MPa (10%) Table 3 Average sandstone depth and overpressure Sandstone Average depth (m TVDSS) Estimated overpressure (MPa) J J J3/J J Average Percentage of total area

11 P.B. Flemings, J.A. Lupa / Marine and Petroleum Geology 21 (2004) Fig. 15. Estimated sandstone pressure from reservoir geometry (Appendix) vs observed sandstone pressure (a a 0 ). b b 0 delineates the pressure trend in the mudstone (Fig. 9). The J sandstone centroid depth is at 3785 m. The sand pressure isz21.7 MPa at this location. Reservoir pressure is overestimated by 2 MPa with this approach. larger than the actual overpressure (19.65 MPa). We interpret that the misfit is due to the effect of salt beneath the reservoir. Two possible approaches to more accurately predict reservoir pressure might be to gain a 3-D understanding of the mudstone pressure through detailed analysis of seismic velocities or to apply some empirical correction for the effect of having a sandstone body near salt Mudstone pressure vs sandstone pressure In the modeled well profiles, pressure is continuous from the mudstone into the sandstone (Fig. 12b). However, porosity-based predictions record an abrupt overpressure jump at the J sandstone-mudstone interface (Figs. 6 and 9). We propose two reasons for this difference. First, because we project the mudstone porosity and pressure from as much as 200 m from the sandstone (Fig. 6), we may not capture the rapid change in pressure near the sandstone body. When the mudstone layer-parallel permeability is much greater than the layer-perpendicular permeability, the change in pressure between the sandstone and the mudstone will occur over a very narrow distance. This effect may be observed near the sandstone body in the A4-BP well where there is a rapid decrease in porosity near the sandstone (Fig. 7c). Second, in regions where the sandstone pressure is greater than the mudstone pressure, it is possible that the present effective stress is less than the maximum past effective stress; in these cases, the pore pressure will be underestimated when based on porosity (Flemings et al., 2002). This may account for the fact that projected mudstone pressures are lower than the sandstone pressures in the up-dip wells (Fig. 7a). 6. Conclusions We compared porosity-based mudstone pressure predictions with observations of in situ pressure in the Bullwinkle minibasin, Gulf of Mexico. This basin underwent extremely rapid Late Pleistocene sedimentation and as a result, the shallow sedimentary section is overpressured. Consequently, observations of porosity vs depth in the shallow sedimentary section cannot be used to derive the compaction parameters that are used to predict pressure. Instead, these parameters must be derived from direct pressure measurements. We used steady-state flow modeling to understand how reservoir geometry and the presence of salt controls reservoir pressures. In the J sandstone package, flow is focussed into the base of the bowl-shaped basin and expelled out its crests. Comparison of 2-D with 3-D basin geometries shows that 3-D cone-shaped bodies have a lower pressure than 2-D V shaped bodies. The presence of a low permeability salt layer beneath the reservoirs shields them from higher pressures, because flow is focussed away from the sandstone beneath the salt layer. Pressures are lower within the Bullwinkle minibasin than at equivalent depths outside the minibasin and we suggest that the underlying salt layer causes this. An approximate empirical approach that incorporates reservoir geometry into pressure prediction is to assume that the sandstone pressure is equal to the area-weighted average of the mudstone pressure. If the mudstone pressure gradient is constant, the sandstone overpressure is equal to the mudstone pressure at its average, or centroid, depth. For the Bullwinkle example, pore pressures predicted by this approach exceed by 10% the actual pressures and we infer the discrepancy to result from the underlying salt. Thus, overpressures predicted from geometry provide an upper bound estimation. Acknowledgements We thank Shell Exploration and Production Company for supplying the data and for permission to publish. M. Maler, G. Bowers, and M. Rowan provided insight into

12 1322 P.B. Flemings, J.A. Lupa / Marine and Petroleum Geology 21 (2004) the deepwater GOM and salt tectonics. B. Dugan and two unnamed reviewers provided excellent reviews. This work was funded by the Penn State GeoFluidsI and II Consortiums (Amerada Hess, Anadarko Petroleum, BHP, Burlington Resources, ChevronTexaco, Devon Energy, ExxonMobil, EnCana, ConocoPhillips, Shell, Unocal). Appendix. Estimation of reservoir pressure An empirical approach to estimate the reservoir overpressure ðp wþ from the bounding mudstone pressure ðp msþ is to assume P w is equal to the area-weighted average of the mudstone overpressure Ð P P w Z ms ðaþda ; (A.1) A where P ms (A) is the pressure at any location (da) onthe reservoir surface and A is the total area of the sandstone body. Under the limiting condition that P ms is proportional to depth P ms Z P o ms CCz; (A.2) where C is the pressure gradient, then Eq. 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