Beth B. Stump(1), Peter B. Flemings(1), Thomas Finkbeiner(2), Mark D. Zoback(2)

Transcription

1 Pressure Differences Between Overpressured Sands and Bounding Shales of the Eugene Island 33 field (Offshore Louisiana, U.S.A.) with Implications for Fluid Flow induced by Sediment Loading Beth B. Stump(1), Peter B. Flemings(1), Thomas Finkbeiner(2), Mark D. Zoback(2) (1) Department of Geosciences, 436 Deike Building, The Pennsylvania State University, University Park, PA 1682 (2) Department of Geophysics, Stanford University, Stanford, CA Abstract We document pressure differences between adjacent sands and shales in geopressured Plio-Pleistocene strata of offshore Louisiana and we quantify a sediment loading model that describes the origin of these differences. The JD sand is in moderate geopressure (Pf/σl.6) and has a lower pressure than its bounding shale. The L1 sand is severely overpressured (Pf/σl.9) and has a pressure greater than its bounding shale. Shales which are adjacent to the JD and L1 sands have pressures (derived from a porosity-effective stress relationship) which follow a lithostatic gradient. We interpret this behavior to result from rapid, spatially varying loading of permeable sand bodies by relatively impermeable shales. Under these conditions, pore pressures at the peak of structure can significantly exceed the pore pressure of bounding shales. The L1 sand records this behavior. In contrast, the low relative pressures in the JD sand may record dissipation of pressure by fluid migration along permeable pathways. The sediment loading model predicts along-stratal flow within sands and cross-stratal flow at structural highs. In a companion paper, Finkbeiner et al. (this volume) describe how sediment loading and the buoyant effect of hydrocarbons combine to drive sand pressures toward the minimum principal stress of bounding cap rocks, resulting in fluid migration. Introduction Shale porosity or some proxy of porosity (e.g. resistivity) has long been used to estimate in situ fluid pressure (Athy, 193; Rubey and Hubbert, 1959; Wallace, 1965; Hottman and Johnson, 1965). The typical approach is to examine the porosity profile in a zone of known fluid pressure (i.e. the hydrostatic zone) and then use this empirical relationship to predict pressure where it is unknown (i.e. the geopressured zone). The resulting predictions are then compared to in situ measurements of fluid pressure. A difference between predicted and measured pressures was interpreted simply as a deficiency of the model. More recently, differences between porosity-derived shale pressures and in situ sand pressures have been interpreted as indicative of late-stage increases in fluid pressure which are not recorded in the shale porosity signature. This effect, termed 'unloading' because it results in a net decrease in effective stress, was developed by Bowers (1994) and further explored by Hart et al. (1995) and Gordon and Flemings (in press). These studies assumed, a priori, that sand pressures were equivalent to shale pressures and interpreted any discrepancy to result from the inadequacy of the porosity-effective stress model. According to the unloading model, a late-stage decrease in effective stress does not result in decompaction (i.e. porosity rebound) along the initial compaction (porosity-effective stress) curve. As a result, the porosity-effective stress model does not successfully predict fluid pressures in sediments with this unloaded deformation path. This study continues to explore the differences between shale-predicted pore pressures and in situ pressures in adjacent sands. Unlike previous work, we interpret the observed deviations between measurements and predictions as actual differences between sand and shale pressures. We first

2 document this behavior in moderate and severely overpressured sands and shales in the Eugene Island 33 (E.I. 33) field (offshore Louisiana, U.S.A.). We then quantify a model which predicts pressure differences in sands and shales that result from the history and geometry of sediment loading. Lastly, we integrate the observations into the sediment loading model to predict the pressure evolution of two sands in the E.I. 33 area. Estimating Shale Pressures We employ a long-recognized technique for estimating fluid pressure from porosity. Terzaghi and Peck (1948) proposed a relationship between porosity and vertical effective stress, and a variety of approaches have been developed to quantify this relationship (Athy, 193; Terzaghi, 1943; Rubey and Hubbert, 1959; Palciauskas and Domenico, 1989). We combine the definition of effective stress (Equation 1) and the porosity-effective stress relationship developed by Rubey and Hubbert (1959) (Equation 2) to calculate fluid pressure from porosity in shales (Equation 3) (Hart et al.). Table 1 describes all of the variables and constants used in this paper. (1) σ v S v P f (2) φ φ e βσ v 1 φ (3) P f S v -- β ln φ Lithostatic stress (σl) is calculated by integrating the wireline bulk density log. Porosity is calculated from the wireline sonic (travel time) log using an empirical relationship first developed by Raymer et al. (198) and then enhanced by Raiga-Clemenceau et al. (1986). t ma (4) φ x t In Equation 4, tma is travel time for the matrix, t is log-derived travel time, and x is an acoustic formation factor. Issler (1992) determined tma to be 22 µs/m and x to be 2.19 for non-calcareous, low total organic carbon shales. We took travel time measurements during deformation experiments on shale core from E.I. 33 which indicate similar values for acoustic formation factor. We plot porosity versus vertical effective stress (Figure 2) in the hydrostatic zone to determine φ and β (Equation 2) and then apply these coefficients (Equation 3) to calculate fluid pressure in the deeper, geopressured section of the well. Results Shale pressures were evaluated for ten wells in this study (Figure 1). We compare our predicted shale pressures with pressure measurements made in adjacent sands (Figure 3, points a and b). In hydrocarbon-bearing sands the pressure of the hydrocarbon phase often exceeds the water phase pressure in the sand (due to fluid density differences). Since we assume that shales have a low (near-zero) hydrocarbon saturation, we interpret the predicted shale pressure to be a water phase pressure (Pw) and calculate water phase pressure in the sand for comparison. Our results show that even after removing the buoyant effect of the hydrocarbon column, pressure in geopressured sands exceeds that in the bounding shales (Figure 3). Figures 4a,b illustrate the general stratigraphy and pressure profile of the E.I. 33 area. This field consists of interbedded Plio-Pleistocene sands and shales. Pressures from measurements, mud

3 weights, and porosity predictions reflect the same general pressure signature. This area is hydrostatically pressured at shallow depth, moderately overpressured at intermediate depth (JD horizon), and severely overpressured at the depth of the L1 horizon. As explored in Gordon and Flemings (in press), the depth at which geopressure is encountered in the upthrown (316 A-1) well is shallower (~19 m) than in the downthrown (331 #1) well (~24 m). We present detailed results for the JD and L1 horizons. The key observation is that shale pressures exceed measurements in the JD sand (Figure 4a), but are less than observed sand pressures at the L1 level (Figure 4b). A cross-plot of measured vs. predicted overpressures (P* Pf -Ph) for all of the wells in this analysis (Figure 5) shows that predicted shale pressures (Figure 3, point a) exceed measurements (Figure 3, point b) in moderately overpressured sands (e.g. less than 7 MPa), and consistently underestimate measurements in severe overpressure (e.g. greater than 15 MPa). If the wireline relationship accurately predicts shale pressure, then sand pressure is not equal to the pressure in the bounding shale. Sediment Loading Model If a permeable sand is loaded asymmetrically by relatively impermeable shales, the consequent sand and shale pressures will differ (Dickinson, 1953; England, 1987; Traugott, 1994). The sand will maintain a hydrostatic pressure gradient while the shale maintains a nearly lithostatic pressure gradient. We illustrate this behavior for sands which are buried to form anticlinal, homoclinal, and synclinal structures (Figures 6a,b,c). In all cases, the pressure gradient within the sand is hydrostatic, and the overpressure (DP*) is the pressure necessary to support the total overburden load. As we show in the Appendix, DP* is a function of the overburden, and the fluid and bulk compressibility (Equation 5). L β (5) DP ρb ρ β+ β f ( 1 φ) f g z( x) dx The pressure profile for the three structures (Figure 6d) shows that the amount of overpressure within the sand (DP*) and the depth at which the sand and shale pressures are in equilibrium (Figure 6d, triangles) are affected by sand geometry. A synclinal sand (Figure 6c) sustains a higher amount of overpressure than an anticlinal sand (Figure 6a). This is logical, because the synclinal sand is supporting a greater load of sediment. As a result, the depth at which the sand is in pressure equilibrium with the overlying shale (termed the centroid by Traugott, 1994) varies with structural geometry. Figure 6d also illustrates that the relationship between sand and shale pressure changes with position on relief. At the structural peak, sand pressures are greater than shale pressure; at the structural low, shale pressure exceeds sand pressure. Case Study: The JD and L1 Sands We explore the distribution of shale and sand pressures as a function of relief along two horizons in the E.I. 33 field: the moderately overpressured JD (Pf/σl.6) and the severely overpressured L1 (Pf/σl.9) (Figures 7a,b). The JD sand dips from ~178 m (585 ft) to ~27 m (68 ft), for a total relief of 29 m. Fluid pressure (Pw) within the JD sand follows a hydrostatic gradient (Figure 7a). Pressures in the bounding shale follow a lithostatic gradient, and exceed sand pressure at most depths on structure. At the peak of structure, sand pressure exceeds shale pressure by approximately 1.4 MPa (~2 psi); at the structural low, shale pressure is 4.7 MPa (676 psi) greater than sand pressure. The sand and shale pressures are in equilibrium at 1836 m (625 ft).

4 The water phase pressure in the L1 (Figure 7b) also follows the hydrostatic gradient while shale pressure follows the lithostatic gradient. The key distinction between this horizon and the aforementioned JD is that sand pressures at the L1 horizon exceed shale pressures at all depths on structure. At the structural peak (195 m; 64 ft), the sand pressure is nearly 4 MPa (574 psi) greater than that of the overlying shale. Sand and shale pressures converge at the base of the sand (2316 m; 76 ft). These observations support the sediment loading model presented above. However, not all of the observations made in the JD and L1 sand are explained by the initial simple model. For example, the depth at which sand and shale pressures are in equilibrium is much lower on structure at the L1 horizon. As a result, the pressure difference between sand and shale is much larger at the top of the L1 than at the top of the JD (4 MPa vs. 1.4 MPa). In addition, while the shale pressures follow the lithostatic gradient, their absolute pressure values are different; the fluid pressure at the JD level is lower than at the L1 level (Pf/σl.6 and.9, respectively). Below we present a model to describe the evolution of pressure and stress in the JD and L1 sands. Discussion Our modified sediment loading model is illustrated in Figure 8. Initially, as the sand is buried by shale, both layers are able to expel their pore fluids and remain hydrostatically pressured (Figure 8a). This expulsion of fluid is possible because the sedimentation rate is slow (Alexander and Flemings, 1995), and the newly deposited material has sufficient permeability. Then, at a critical depth, the system becomes effectively sealed and ceases to expel fluids (Figure 8b). This transition may be caused by a sudden drop in the shale permeability as porosity drops beneath a critical level (Mello et al., 1994; Gordon and Flemings, in press), or it may be due to an increase in sedimentation rate (Alexander and Flemings, 1995). Once the system becomes sealed, fluid pressure in both the sand and bounding shale increases at a nearly lithostatic gradient (Figure 8b). Ultimately, there is a spatial variation in sedimentation and the consequent generation of structural relief (Figure 8c). Fluid pressure within the permeable sand follows the hydrostatic gradient; shale fluid pressures track the lithostatic gradient. Therefore, as relief is generated, the pore pressures in the sand at the top of structure begin to exceed pressures in the bounding shales. If the top of the sand is permeable and connected to other permeable layers (e.g. adjacent to a permeable fault zone) or if the pressure in the sand exceeds the minimum principal stress of the bounding shale, fluids will migrate out of the sand, thereby decreasing the sand pressure. This effect of pressure bleed-off is shown in Figure 8d, as the line representing sand pressure shifts to the left and overpressure (DP*) decreases. Figures 9a and 9b illustrate our models for pressure evolution in the JD and L1 sands. Following Hart et al. (1995), we present the simplest model in which sand pressure increases hydrostatically (t 1 to t 2 ) until a depth at which it begins to increase at a nearly lithostatic gradient (t 2 to t 3 ). The actual pressure path is unknown; pressure may have increased at a gradient between hydrostatic and lithostatic (Figure 9a, dashed lines). Both the absolute sand pressure and the difference between sand and shale pressures at the top of structure are lower at the JD level (Figure 9a) than at the L1 horizon (Figure 9b). The JD appears to record a greater pressure bleed-off, even though pressures are well below the fracture gradient of the cap rock (Finkbeiner et al., this volume). This implies that fluid migration occurred along permeable pathways (Alexander and Handschy, in press), rather than by hydrofracture. The sediments which overlie the JD have a higher permeability than the stratigraphically deeper sediments (e.g. which directly overlie the L1), allowing more vertical fluid flow and greater pressure dissipation.

5 In contrast, at the L1 level, the depth at which sand and shale pressures are equal is much lower on structure, indicating that pressure dissipation has been negligible. In Figure 8d, we do not see any decrease in overpressure through time. However, Finkbeiner et al. (this volume) suggest that fluid pressure in the L1 sand is controlled by the minimum horizontal stress in the overlying shale. Any pressure greater than the current level will bleed off by natural hydraulic fracture. We emphasize that the sediment loading model relies heavily on at least three assumptions. First and foremost, shales are assumed to be relatively impermeable. By this we mean that shale pressures will not dissipate significantly over the time scales of sediment loading. In this regard, it is reassuring that shale pressures record a lithostatic gradient. Second, we assume that sediment loading is the dominant source of overpressure. This was documented in detail by Gordon and Flemings (in press) for the E.I. 33 area. However, we recognize that other pressure sources are possible. All of these assumptions are most appropriate for young, rapidly loaded basins; it is not apparent to us if this model is appropriate in older basins. Our final assumption is that wireline predictions of shale pressure are correct. For this to be true, compressibility must be constant with depth, effective stress must always increase (i.e. ignores unloading effect), and the sonic log must be an accurate measurement of porosity. In the latter regard, we emphasize that we have produced similar results with the bulk density log. Hart et al. (1995) estimated that compressibility must be greater than twice the value calculated from the hydrostatic zone to replicate the severe overpressures observed at depth. The integration of sand and shale pressure characterization into the sediment loading model provides insight into not only the present pressure state of sands and shales but also into the evolution of pressure, stress, and fluid flow through time. In particular, our results emphasize that crossstratal flow (i.e. near vertical) is dominant at structural highs, where the difference between sand and shale pressures is a maximum. This cross-stratal flow is driven by the lateral flow as sands compact in response to the applied overburden load. Furthermore, flow occurs most rapidly during sedimentation events. Conclusions Differential sediment loading of a permeable sand can result in fluid pressures which differ from those in overlying shales. These pressure differences are documented using porosity-derived shale pressures and measured sand pressures for ten wells in the E.I. 33 area. We present a quantitative sediment loading model to explain the observed differences and provide a method of calculating sand pressure as a function of structural geometry and total relief. This model allows us to gain insight into the evolution of pressure, stress, and fluid flow in the basin. This approach has the potential to provide insight into trap quality and the history of secondary migration. Acknowledgments This research is supported by the Gas Research Institute. We would like to thank Pennzoil, Shell, and Texaco for generously providing the data used in this analysis, as well as Martin Traugott (Amoco) for his insight into the effect of structural relief on fluid pressure.

6 Table 1: Nomenclature Name Value Description g 9.8 gravitational acceleration (m/ s 2 ) P* variable overpressure (MPa) Pf variable fluid pressure (MPa) Ph.15*depth(m) hydrostatic fluid pressure (MPa) Pw variable water phase pressure (MPa) x 2.19 acoustic formation factor β 3.13E-2 matrix compressibility (MPa- 1 ) βf 4.88E-4 fluid compressibility (MPa -1 ) tma 22 matrix travel time (µs/m) t variable log-derived travel time (µs/m) φ variable wireline-derived porosity φ.386 reference porosity ρb variable bulk density (kg/m 3 ) ρf 17 fluid density (kg/m 3 ) σl variable lithostatic stress (MPa) σv variable vertical effective stress (MPa) Appendix: Derivation of Undrained Sediment Loading Model Consider a material element (contains a constant number of solid grains) which remains undrained (i.e. no fluids escape) that is loaded from above with a stress Dσl. This stress is balanced by an opposing stress which is the combination of change in fluid pressure (DPf) and the change in vertical effective stress (Dσv) in the material element. (A1) β ( φ) β β DS f v φ DP ( β β )Dσ f f s v Equation A1 is derived in Gordon and Flemings (in press) who built on the derivation of Palciauskas and Domenico (1989). Equation A1 assumes: 1) the solid grains are incompressible and the fluid and matrix are linearly compressible {(1/ρf)Dρf βfdpf;dφ-βφdσv}; 2) strain is uniaxial; and 3) there are no temperature effects.

7 Consider the same material element buried a depth dz: (A2) DS v ρ b gdz (A3) DP f ρ f gdz( x) + P (A4) Dσ v ρ b gz ( ρ f gdz + DP ) Substituting Equations A2, A3, A4 into Equation A1, and solving for the change in fluid pressure, we find: (A5) DP f ρ β β f ( 1 φ) + β gdz b In our work in Plio-Pleistocene strata of the Eugene Island area, typical bulk compressibility and porosity values are 3.13E-2 MPa -1 and.3, respectively (Hart et al., 1995, Gordon and Flemings, in press), while fluid compressibility is 4.88E-4 MPa -1 (de Marsily, 1986). Using these values, Equation A5 reduces to: (A6) DP f.989ρ b gdz Thus, the change in fluid pressure (DPf) supports ~99% of the change in the overburden load (Dσl). Consider next the problem of a sand body of length L that has been buried to a variable depth z, where z f(x) (Figure A1). The sand is composed of material elements of length dx. We assume that the fluid can be displaced within the sand (qw), but that no fluid leaves the sand body. Under this constraint, balance of stress requires: (A7) β ( φ) β DS f v ( x) β DP( x) β 1 φ f Dσ v ( x) ρ ρ f qx ( ) f In this case, the changes in fluid pressure, overburden, and effective stress are: (A8) DS v ρ b gdz( x) (A9) DP f ρ f gdz( x) + DP (A1) Dσ v ρ b gdz( x) ( ρ f gdz( x) + DP ) Substituting Equations A8-A1 into Equation A7 and integrating over the length of the sand body

8 L, we find: (A11) L L L L β ( φ) β β f DS v ( x) ( φ) DP x 1 ( ) β f f Dσ v ( x) ρ ρ f qx ( ) f overburden load fluid pressure effective stress flow term Because we assume that the entire sand body is undrained, the integral of the flow term is equal to zero. Upon integration, and solving for the change in overpressure resulting from structural relief, we find: L β (A12) DP ρb ρ β+ β f ( 1 φ) f g z( x) dx Equation A12 can be solved for any load geometry (z(x) f(x)) to estimate the overpressure (DP*) added to the system. For example, in the main body of this paper, we describe three possible functions for z(x): linear, hyperbolic, and parabolic (Figure 6). References Alexander, L.L., and P.B. Flemings, 1995, Geologic Evolution of a Plio-Pleistocene Salt-Withdrawal Minibasin: Eugene Island Block 33, Offshore Louisiana: AAPG Bulletin, v. 79, no. 12, pp Alexander, L.L., and J.W. Handschy, in press, Fluid Flow in a Faulted Reservoir System: Fault Trap Analysis for the Block 33 Field in Eugene Island South Addition, Offshore Louisiana: American Association of Petroleum Geologists Bulletin, v. 82. Athy, L.F., 193, Density, porosity, and compaction of sedimentary rocks: American Association of Petroleum Geologists Bulletin, v. 14, no. 1, p Bowers, G.L., 1994, Pore pressure estimation from velocity data: Accounting for overpressure mechanisms besides undercompaction: Society of Petroleum Engineers Paper 27488, p de Marsily, G., 1986, Quantitative Hydrogeology: Groundwater Hydrology for Engineers, Academic Press, Inc., 592 pp. Dickinson, G., 1953, Geological aspects of abnormal reservoir pressures in Gulf Coast Louisiana: AAPG Bulletin, v. 37, no. 1, pp England, W.A., A.S. MacKenzie, D.M. Mann, and T.M. Quigley, 1987, The movement and entrapment of petroleum fluids in the subsurface: Journal of the Geological Society, London, 144, pp Finkbeiner, T., M.D. Zoback, B.B. Stump, and P.B. Flemings, 1998, In situ stress, pore pressure, and hydrocarbon migration in the South Eugene Island Field, Gulf of Mexico: this volume.

9 Gordon, D.S. and P.B. Flemings, in press, Generation of Overpressure and Compaction-Driven Fluid Flow in a Plio-Pleistocene Growth-Faulted Basin, Eugene Island 33, Offshore Louisiana: Basin Research. Hart, B.S., P.B. Flemings, and A. Deshpande, 1995, Porosity and pressure: Role of compaction disequilibrium in the development of geopressures in a Gulf Coast Pleistocene basin: Geology, v. 23, no. 1, pp Holland, D.S., W.E. Nunan, and D.R. Lammlein, 199, Eugene Island Block 33 field- U.S.A., offshore Louisiana, in E.A. Beaumont and N.H. Foster, eds. Structural traps III, tectonic fold and fault traps: AAPG Treatise of Petroleum Geology, Atlas of Oil and Gas Fields, p Hottman, C.E. and R.K. Johnson, 1965, Estimation of formation pressure from log-derived shale properties: Journal of Petroleum Technology, v. 17, Issler, D.R., 1992, A new approach to shale compaction and stratigraphic restoration, Beaufort- Mackenzie basin and Mackenzie Corridor, northern Canada: American Association of Petroleum Geologists Bulletin, v. 76, no. 8, p Mello, U.T., G.D. Karner, and R.N. Anderson, 1994, A physical explanation for the positioning of the depth to the top of overpressure in shale-dominated sequences in the Gulf Coast basin, United States: Journal of Geophysical Research, v. 99, no. B2, pp Palciauskas, V.V., and P.A. Domenico, 1989, Fluid pressures in deforming porous rocks: Water Resources Research, v. 25, no. 2,. pp Raiga-Clemenceau, J., J.P. Martin, and S. Nicoletis, 1986, The concept of acoustic formation factor for more accurate porosity determination from sonic transit time data: SPWLA 27th Annual Logging Symposium Transactions, Paper G. Raymer, L.L., E.R. Hunt, and J.S. Gardner, 198, An improved sonic transit time-to-porosity transform: SPWLA 21th Annual Logging Symposium Transactions, Paper P. Rubey, W.W. and M.K. Hubbert, 1959, Overthrust belt in geosynclinal area of western Wyoming in light of fluid pressure hypothesis, 2: Role of fluid pressure in mechanics of overthrust faulting: Geological Society of America Bulletin, v. 7, p Terzaghi, 1943, Theoretical Soil Mechanics: New York, John Wiley and Sons, Inc., 51 p. Terzaghi, K. and R.B. Peck, 1948, Soil mechanics in engineering practice: New York, John Wiley and Sons, Inc., 566 p. Traugott, M.O., 1994, Prediction of pore pressure before and after drilling-- taking the risk out of drilling overpressured prospects: American Association of Petroleum Geologists Hedberg Research Conference, Denver. Wallace, W.E., 1965, Abnormal surface pressure measurements from conductivity or resistivity logs: Oil & Gas Journal, v. 63, pp

10 Figure Captions Figure 1: The E.I. 33 field is in the Gulf of Mexico, 272 km southwest of New Orleans, LA, U.S.A. at a water depth of ~77 m (Holland et al., 199). We use wireline and pressure data from 1 wells in this field. Plus symbols indicate straight holes; solid lines represent deviated well paths; filled circles show the bottom hole locations of deviated wells. Figure 2: Log-linear plot of sonic-derived porosity (φ) versus vertical effective stress (σv) in the hydrostatic zone for the 331 #1 well (located in Figure 1). Lithostatic stress (σl) is calculated by integrating the bulk density log; hydrostatic pressure is calculated from a gradient of.15 MPa/ m (.465 psi/ft) for sea water. Solid line represents the regression fit to the data. Figure 3: In this study we compare porosity-predicted shale pressures (point a) with water phase pressures (point b) in adjacent sands. Water phase pressures are used in order to negate the buoyant effect of the hydrocarbon column. Figure 4a,b: Gamma ray log and pressure profiles for the 331 #1 and 316 A-1 wells (located in Figure 1). The JD and L1 sands are interpreted in both wells. In the 331 #1 well, the L1 is faulted out and the approximate location of the L1 horizon is shown. These wells are on opposite sides of a large growth fault; the #1 well is on the downthrown side of the fault, while the A-1 is upthrown. This explains the offset between the horizons at the two wells (~56 m at JD level; ~98 m at L1 level). On the pressure track, bounding lines are hydrostatic pressure (.465 psi/ft) and lithostatic stress (calculated by integrating the bulk density log). Plus symbols represent porosity-predicted shale pore pressures; filled circles represent measured in situ pressures in adjacent sands. Overpressure calculated from drilling mud weights is shown by white fill; vertical effective stress is the light gray area. Figure 5: Cross plot of sand and shale overpressures shows that in severe overpressure sands are more highly pressured than shales, but at shallow depths (low values of overpressure) shale pressures exceed sand pressures. All sand overpressures are calculated in the water phase (Pw), so the sand pressures in excess of adjacent shale pressures can not be attributed to the buoyant effect of a hydrocarbon column. Dashed line represents a one-to-one correlation; solid line is a regression fit for these data (y.673x , R 2.94). Figure 6: Pressure evolution in three different sand structures: a) anticlinal (z(x) x 2 /3), b) homoclinal, c) synclinal (z(x) (2/3)x 1/2 ). d) Pressure profile resulting from 1,' of relief on three different structures. The amount of overpressure generated by structure (DP*) is dependent on the overburden load; synclinal structure supports the most sediment, therefore the amount of overpressure is greatest. Dashed lines represent hydrostatic pressure (.15 MPa/m;.465 psi/ ft) and lithostatic stress (.21 MPa/m;.94 psi/ft). Points 4,6,8 represent sand pressures at top of structure; points 5,7,9 represent sand pressures at the base of structure. Points 2 and 3 represent shale pressure at top and bottom of structure, respectively. Triangles highlight depth at which sand and shale pressure are in equilibrium ("centroid"). The line representing the shale pressure (solid) nearly overlies the lithostatic stress line (dashed), but the difference can be seen at depths greater than 13, feet. Figure 7: Pressure plots for sands and shales at the JD and L1 horizons. a) At the moderately pressured JD sand, shale pressure exceeds sand pressure at most points on structure. Pressure gradient within sand is hydrostatic; shale pressure gradient is approximately lithostatic. b) At the L1 level, sand pressure is greater than shale pressure; pressures converge at the base of structure. Sand and

11 shale pressure gradients are similar to those at JD horizon. Shale pressure is represented by filled circles; plus symbols represent sand pressure. The lithostatic gradient (.21 MPa/m) is shown for reference. Figure 8: Schematic of pressure evolution in sand and bounding shale. a) At time 1, sand and shale are hydrostatically pressured at some depth, z1. b) Sand layer is buried from z1 to z2; pressures in both sand and shale increase at lithostatic gradient. c) Lateral variation in sedimentation rates causes sand to dip; sand and shale pressures at top of structure diverge. d) Fluid bleeds out of sand; sand pressure decreases and converges on shale pressure at the top of structure. Figure 9: Model for pressure evolution in the JD and L1 sands shows a hydrostatic increase in pressure from t 1 to t 2, and a nearly lithostatic increase in pressure from t 2 to t 3. Following t 3, as structure is generated in the sands, sand fluid pressure begins to exceed shale pressure. Dashed lines represent alternative pressure paths. a) Sand pressure in the JD decreases as fluid is bled off (t 3 to t 4 ). b) Sand pressure remains greater than pressure in overlying shale (no dissipation is observed). A1: Two-dimensional model in which the sand parcel has pressure communication with the rest of the layer.

12 MISSISSIPPI N LOUISIANA New Orleans Eugene Island B A-2ST2 A-22 A-4 #1 B-13 A-6 A-1 A #5 3 miles (4.8 km) Figure 1 Shale Porosity Vertical Effective Stress (psi) φ.386e -2 -(3.13x1 σ) Vertical Effective Stress (MPa) Figure 2

13 shale gas a b a Pressure (MPa) b P w P cow P o P cog P g 195 Depth (ft) 66 Depth (m) water oil G/O contact P o 3756 O/W contact P w Pressure (psi) Figure 3 a) b) Subsea True Vertical Depth (feet) #1 Pressure Gamma Ray (MPa) 2 7 JD L1 Predicted from φ Measured in situ Subsea True Vertical Depth (meters) Subsea True Vertical Depth (feet) Gamma Ray Pressure (MPa) 2 5 Predicted from φ Measured in situ A-1 JD L Subsea True Vertical Depth (meters) Figure 4

14 Calculated Shale Overpressure (psi) Measured Sand Overpressure (MPa) shale pressures higher than sand pressures shale pressures lower than sand pressures Measured Sand Overpressure (psi) Calculated Shale Overpressure (MPa) Figure 5 Time 1 a) b) c) 1 shale 1 sand shale 1 land surface land surface land surface Time Pressure (MPa) hydrostatic pressure Depth (ft) DP* a DP* b DP* c 5 lithostatic stress Depth (m) Pressure (psi) Figure 6

15 a) b) Sand and Shale Pressures at the JD Horizon Subsea TVD (ft) 55 6 Fluid Pressure (MPa) Pressure diff. at top 1.36MPa (198 psi) + hydrostatic gradient JD Sand Top lithostatic gradient (.21 MPa/m) gradient.3 MPa/m Sand Shale Fluid Pressure (psi) Subsea TVD (m) Subsea TVD (ft) Figure Sand and Shale Pressures at the L1 Horizon Fluid Pressure (MPa) Pressure diff. at top 3.96 MPa (574 psi) lithostatic gradient (.21 MPa/m) hydrostatic gradient + + gradient.21 MPa/m 22 + Sand Shale Fluid Pressure (psi) + L1 Sand Top Subsea TVD (m) a) b) Time 1 (t 1 ) Time 2 (t ) 2 Pressure Pressure shale pressure sand pressure added sediment thickness shale pressure sand pressure z 1 Depth t 1 hydrostatic pressure lithostatic stress z 1 Depth t 1 hydrostatic pressure z 2 lithostatic stress t 2 c) Time 3 (t 3 ) d) added sediment thickness z 1 z 2 Depth Pressure t 1 z 3 hydrostatic pressure shale pressure sand pressure lithostatic stress Time 4 (t ) 4 Pressure z 1 Depth t 1 hydrostatic pressure shale pressure sand pressure t 2 sand DP* t3 z 2 z 3 lithostatic stress t t 3 4 sand DP* Figure 8

16 Subsea TVD (ft) a) b) t 1 Evolution of Pressure in the JD Sand Fluid Pressure (MPa) t 2 t 4 t 3 shale pressure sand pressure Fluid Pressure (psi) Subsea TVD (m) Subsea TVD (ft) Evolution of Pressure in the L1 Sand Fluid Pressure (MPa) t 1 shale pressure sand pressure t 2 t Fluid Pressure (psi) Subsea TVD (m) Figure 9 no flow x land surface Sv q w q w z L Figure A1 dx no flow