PRESSURE (P), OVERBURDEN (Sv), AND MINIMUM HORIZONTAL STRESS (Shmin) IN EUGENE ISLAND BLOCK 330, OFFSHORE GULF

OF MEXICO TOPICAL REPORT NUMBER 1 (APRIL 1, 1996 - JULY 1, 1996)

GRI-96/0285

Prepared by:

T. Finkbeiner, B.B. Stump, M.D. Zoback, and P.B. Flemings The Pennsylvania State University 543 Deike Building University Park, PA 16802

For: GAS RESEARCH INSTITUTE Contract Number: 5095-260-3558

GRI Project Manager Richard A. Parker Basic Research Division

Research Summary

Title: Pressure (Pp), Overburden (Sv), and Minimum Horizontal Stress (Shmin) in Eugene Island Block 330, Offshore Gulf of Mexico

Contractor: The Pennsylvania State University, with a subcontract to Stanford University

GRI Contract Number: 5095-260-3558

Principal Investigator: Peter B. Flemings

Report Period: 4/1/96 to 7/1/96 Topical Report

Objective: The objectives of this study were: 1) characterize minimum principal stress (Shmin), pore pressure (Pp), and overburden (Sv); and 2) characterize the interrelationships between these 3 variables based on available leak-off test (LOT) and fracture completion data within the EI-330 field.

Benefits: 1. There are few detailed published analyses examining in situ stress data from both sands and shales. Results from this analysis may yield insight into: a) optimizing drilling programs (i.e. casing points, mud programs); b) minimizing fracture completion costs (through an understanding of expected stress state in sands and shales); c) predicting seal integrity in exploration settings.

2. Overburden gradients based on wireline density logs are significantly less (~0.93 psi/ft) than the commonly-assumed 1 psi/ft. We recommend calculating it for each area of study.

3. Precisely-recorded leak-off and fracture completion test data may be used to characterize minimum horizontal stress and pore pressure.

4. The data presented in this report can be used to define a field-specific (EI-330) fracture gradient model.

Technical Perspective: Fracture completions have become popular in poorly consolidated sediments in order to maximize borehole stability and production rates. Few fields contain extensive fracture completions and thus few data compilations exist which constrain pressure (Pp), overburden stress (Sv), and minimum principal stress (Shmin). The EI-330 field, the subject of this study, contains 22 fracture completions to date. Careful characterization of this dataset has the potential to: 1) Develop a stress model to reduce the cost of fracture completions (by eliminating the need for a pre-frac stress measurement); 2) better constrain the fracture gradient to assure borehole stability and minimize drilling costs; and 3) risk fault seal ahead of the drill bit through an understanding of the least principal stress behavior.

Results: 1. Effective stress ratio, K, is an average 0.54 for sands and 0.70 for shales.

2. There is no observed trend of increasing K with depth or pressure as is assumed in a variety of previous studies.

3. A model is presented to predict stress evolution with pore pressure drawdown, but empirical data are insufficient to substantiate the model.

Technical Approach: We characterize minimum principal stress (Shmin) and pore pressure (Pp) within reservoir sands (based on fracture completion data) and shales (based on leak-off data) within the Eugene Island South Addition (Figure 1). The availability of minifrac data provides an important advantage over data used in previous studies as accurate least principal stress and pore pressure measurements are available from within the same sand intervals. Leak-off test data, in contrast, are relatively abundant and have frequently been used in attempts to make pore pressure and least horizontal stress predictions. Given the

two different types of data (LOTs and minifracs) available to us, we try to assess how these can be characterized and compared with each other, how they fit previously published fracture gradient models, how they vary with pore pressure and geologic structures, and how they might influence hydrocarbon migration and accumulation.

We evaluated pore pressure (Pp), minimum principal stress (Shmin), and overburden stress (Sv) at each minimum principal stress measurement, and then assessed the errors of these estimates. Next, we characterized relationships between Pp, Sv, and Shmin, and compared these results to previous work. We also compared stress results for sands to those for shales. Lastly, we developed a preliminary analysis of stress evolution during production.

Project Implications: 1. Examination of Pp, Shmin, and Sv in one location reveals that regional empirical fracture gradients cannot accurately predict local fracture gradients. Fracture gradient models should be locally derived where possible.

2. For a given pore pressure, closure stresses (Shmin) are slightly greater in shales than in sands which should lead to some level of fracture containment.

3. The large scatter in pressure and stress data indicates that structure, stratigraphy, and rock properties lead to large spatial variation in stress behavior.

GRI Project Manager Richard Parker Basic Research Division

1. Introduction

Analysis of fracture completion reports and leak-off tests (LOTs) from different wells in the South Eugene Island 330 field (EI-330) demonstrates strong variation in pore pressure (Pp) and minimum horizontal stress (S3 = Shmin). Shmin values within sands and shales range from half of the overburden stress (Sv) to roughly 90% of Sv. Pore pressures vary from sub-hydrostatic to 90% of Sv. Despite these variations, the data can be characterized in the following manner.

An effective stress ratio (K=(Shmin-Pp)/(Sv-Pp)) of approximately 1/3 acts as a lower bound for the observed data. Most of the data record a stress ratio greater than one third which implies that many areas have lower differential stresses than are implied by frictional faulting theory. Sands show a lower mean value for K (0.54) than shales (0.70), which implies higher differential stresses in the sands than in the shales.

Analysis of these data with respect to individual reservoir sands reveals that there may be an important relation between differential stress behavior and age, composition, burial history, and spatial position. Analysis of poroelastic reservoir behavior in response to

fluid production suggests that there are significant changes in stress that accompany production, but it is not supported by the limited data available.

2. Work Performed

Geologic overview The data used in this study were acquired in the Eugene Island 330 (EI-330) field, a Plio-Pleistocene hydrocarbon reservoir contained within a salt-withdrawal minibasin. The geologic evolution of this basin is described by Alexander and Flemings (1995) and the discovery and development of the EI-330 field is described by Holland et al. (1992). The Eugene Island minibasin is bounded to the north by a regional (down to the south) fault system and to the south by an antithetic fault system (Figure 1).

Figure 1: Basemap showing dominant structures of study area at level of OI-sand (refer to figure 2) and trajectories of wells from which data were used in this study (pluses indicate fracture completions, circles LOTs, black squares represent wells used in Figure 3). Line C-C' marks the map view of the cross section in Figure 2.

Hydrocarbons are produced in over 25 different sands which are themselves segmented into at least 100 structurally or stratigraphically distinct reservoirs. The major producers include the GA through OI sandstone (Figures 2 and 3). There is a characteristic increase in overpressure with depth that is stratigraphically controlled. The GA and shallower

sands are near hydrostatic; the JD through LF are moderately overpressured; and the OI and deeper sands reach near lithostatic pressures (Figure 3A and B).

Figure 2: Dip-line well log cross section (marked C-C' in figure 1) in the South Eugene Island field showing the minibasin and footwall separated by normal growth fault system. Sand intervals are shown in gray; dashed lines are the corresponding flooding surfaces. Displayed well logs are either gamma ray or spontaneous potential logs (left) and resistivity logs (right) (from Alexander and Flemings, 1995).

Because overpressures are closely correlated to stratigraphy, offset along normal faults in the minibasin results in abrupt lateral contrasts in fluid pressure. Analysis of the normal fault system with respect to the pore pressure distribution shows that isobars are highly discontinuous across fault segments suggesting the compartmentalization of individual reservoir pockets (Gordon and Flemings, in review).

Figure 3: Type well logs including gamma ray, resistivity, and pore pressure with depth. Pressure was calculated from drilling mud weights. Sand names were correlated from gamma ray logs and seismic data and relate to the same sands as in the dip-line well log cross section (Figure 2). (A): Type log from minibasin well B-13. (B): Type log from well #3 in the footwall of the growth fault system (located in Figure 1). Note the difference in depth to top of overpressure between the well in the minibasin compared to the well in the footwall.

Fracture completion reports and leak-off test data Twenty-two fracture completions and nineteen leak-off test measurements from production wells within the EI-330 field (see basemap, Figure 1) provided pore pressure and least principal stress data (Table A1) used in this study. In the case of the fracture completions, detailed reports allowed us to verify and extract accurate pressure values to assess both least principal stresses and pore pressures. We considered the reported fracture closure pressure (Figure 4) to be closest to the least principal stress. The FCP is calculated from the break in slope of the pressure-time curve after the well has been shut-in and the pressure has bled off to the critical point where it can no longer sustain the least principal stress to keep the minifracture open (Figure 4). At this stage the fracture has propagated far enough into the formation that fracture initiation, near wellbore and fluid-related friction effects during pumping have dissipated, and the pressure recorded should more or less reflect the least principal stress in the reservoir. At least two closure pressure values were generally obtained per test, using G-function (Nolte, 1979) and square root of time plots. In cases where a step-rate test was also run, two more values for Shmin were available. We used the minimum reported closure pressure as the lower bound on Shmin and the highest reported closure pressure as the upper bound. The average Shmin was the arithmetic mean of all of the closure pressure values and the errors were calculated as the difference between mean value and upper/lower bound value. Pore pressure values were usually obtained at the latest stages of each minifracture test, when the well is shut-in, the fracture is closed, and the pressure asymptotically reaches the pore pressure. Again, at least two values were available, allowing us to define upper and lower bounds for subsequent uncertainty calculations.

Figure 4: Bottomhole pressure and pump flow rate vs. time in a typical minifracture test (Gaarenstroom et al., 1993).

Information about the leak-off tests, by contrast, is not nearly as complete. Although a LOT is run every time a section of well is cased, often the driller concludes the test before an actual leak-off occurs. We refer to these tests as Formation Integrity Tests (FITs) and disregarded these data in this study, because of the uncertainty of the data. We only considered tests in which fluid was lost into the hydraulically fractured formation. In

these cases, two pressure values were generally reported: (1) the pressure at which the formation had broken down and a fracture was propagated; (2) the bleed-off pressure after shut-in and time dependent pressure decay. Shut-in pressures which are commonly used to approximate the least principal stress were not available to us. Hence, we decided to use the maximum pressure, which we believe reflects the fracture propagation pressure. Although this pressure is different from the real Shmin value, it is sufficiently close to be used as an upper bound value to Shmin (Figure 4). The bleed-off value was used as a lower bound, but involves larger uncertainties because it was somewhat arbitrarily chosen after shut-in. Also, fluid loss due to diffusion is a major concern, especially in shallow LOTs. This would contribute to further error. Drilling engineers are aware of this problem and are working to adjust pumping rates in areas where this has been shown to be a problem (personal communication, L.J. McClure, Pennzoil, 1996).

Pore pressure calculations for LOT Because of their drastically varying permeability and compaction characteristics, we consider sand and shale LOT data separately (Tables A2 and A3). Lithologic well log data (i.e. gamma ray, spontaneous potential) helped to distinguish between them. For LOTs conducted in permeable reservoir sand units, mud weight data provide an upper bound value for pore pressure because wells in this region are drilled overbalanced with respect to pore pressures in sands to prevent well kicks and blowouts. Pressure surveys within neighboring sand units indicate that on average mud weight overbalances pore pressure by approximately 10%. We used this mean difference to calculate a lower bound for pore pressure in sands by simply deducting 10% from the reported mud weight. Pore pressures in shales may be greater than in nearby sands because the shales have much lower permeabilities and cannot release fluids at sufficient rates during compaction. Since it is nearly impossible to measure pore pressure in shales because of the extremely low permeability, we estimate Pp using mud weight data and porosity-effective stress analysis. We employed a technique used by Hart et al. (1995) to calculate Pp in shales from porosity.

Porosity (f) was calculated from wireline sonic logs (Issler, 1992), and b (compressibility) and f0 (reference porosity) are empirical constants. This method calculates overpressure generated by compaction disequilibrium, but may underestimate actual pore pressure because it does not account for late-stage pressure generation mechanisms such as smectite dehydration (Hart et al., 1995) Therefore, we use porosity-derived pressures as a lower bound for Pp in overpressured shales, and, for lack of any more accurate data, we use mud weight-derived pressure as an upper-bound for Pp in overpressured shales. LOTs at shallow depths were considered to be within the hydrostatic zone. The volumetric fraction of shale at shallow depths in the EI-330 field is not larger than 30% implying only small shale lenses amongst much larger sand bodies. Therefore, these small lenses are assumed to drain hydrostatically with the sands despite the lithologic differences between them. Since the porosity-effective stress methodology is generally believed to give reasonable estimates for hydrostatic pore pressures (Hart et al., 1995), we used it to obtain the lower bound value for Pp. For the upper bound estimate we chose the mud weight equivalent pressure which is expected to overbalance the pressures in the shales under hydrostatic conditions.

Uncertainties were calculated by estimating absolute errors for each parameter. This is the most conservative approach since errors are cumulative when considering quantities such as effective stresses or effective stress ratios.

Overburden stress A necessary step in this analysis is accurate calculation of the overburden stress. Since we expect undercompaction effects at depth resulting in overburden gradients that are considerably lower than the commonly assumed gradient of 1 psi/ft (22.65 MPa/km), the overburden stress was calculated by integrating wireline density logs over depth. Four wells were chosen for this analysis based on hole condition and quality of available well log data - primarily density, sonic, resistivity, and caliper logs. These wells are located in different fault blocks of the growth fault system and would allow us to not only see variations of overburden gradients with depth but also see how they vary laterally. In order to obtain reasonable and continuous density values with depth, caliper logs helped to identify washed-out depth intervals for which the density log was replaced with interpolated values. The weight of the water column (75.6 m deep in this area) was also taken into account. The continuous density profile was integrated, multiplied by the gravitational constant, and then divided by depth to yield the overburden gradient. Figure 5 shows the differences between the results of this approach and the constant (1 psi/ft) overburden gradient assumption. Obviously, the latter method grossly overestimates the true overburden values.

Figure 5: Overburden gradients for four wells used to calculate the overburden stress at fracture completion and LOT depths in the EI-330 field. Note for comparison the often-assumed gradient of 1 psi/ft (22.65 MPa/km).

3. Analysis

Stress and pore pressure variations versus depth The values for pore pressure and minimum horizontal stress (Table A1) are shown in composite figures of pressure and stress vs. depth for sands (Figures 6A, 6B) and shales (Figures 7A, 7B). Large variations in pressure and stress magnitudes are apparent at all depths. This results from the fact that despite their spatial proximity (within or near the same minibasin), different individual reservoirs have varying pressure and stress states. In general, the least principal stress varies from 65% to 100% of lithostatic (Sv) and pore pressures range from sub-hydrostatic to 90% of Sv. As observed in previous compilations of such data (e.g. Anderson et al., 1973; Althaus, 1977; Breckels and van Eekelen, 1981) both pore pressures and least principal stresses (S3 = Shmin) approach the overburden stress with depth. This simultaneously decreases differential and effective stresses with depth. Notice the large uncertainties in pore pressures for overpressured shales (Figure 7A) based on the fact that mud weight data poorly constrain Pp of shales under these conditions.

Figure 6: Average pore pressure (A) and minimum principal stress Shmin (B) for sands as extracted from fracture completion and LOT reports. Error bars denote upper and lower bounds (mostly masked by symbol). Triangles represent fracture completions and squares are LOTs. Lithostatic stress (dashed line) was derived from integrated density logs (331 #1 well) and hydrostatic pressure (solid line) was calculated for brine (0.465 psi/ft = 10.53 MPa/km). The seawater depth in this area is 75.6m.

Sub-hydrostatic pore pressure conditions near 6900 ft (2100m) and 7700 ft (2350m) depth within reservoir sands (Figure 6A) reflect pressure drawdown due to hydrocarbon production. Pressure surveys available to us show a pore pressure decline for the KE-1 sand at 6200 ft (1900m) by 580-870 psi (4-6 MPa) (fault block dependent), for the LF-sand at 6900 ft (2100m) by 1450 psi (10 MPa), and for the OI-sand at 7700 ft (2350m) by

2600 psi (18 MPa). Similar numbers are probably realistic for the IC-4 sand at 5600 ft (1700m), although no drawdown information for this sand is available at present. This observation shows that pore pressure prior to well completion was considerably higher in these reservoir sands and sub-hydrostatic pressure conditions imply a transient pressure response due to hydrocarbon production. We believe that this effect also has a strong influence on the stress state and that Shmin at the time of fracture completion may not represent its original value since stress changes due to fluid extraction are superimposed. The issue of restoring the stress state to its original value will be discussed further below.

Figure 7: Average pore pressure (A) and minimum principal stress Shmin (B) for shales as extracted from LOT reports. Error bars denote upper and lower bounds (mostly masked by symbol). Triangles represent overpressured shales and squares indicate hydrostatic conditions. Lithostatic stress (dashed line) was derived from integrated density logs and hydrostatic pressure (solid line) was calculated with a constant gradient for brine (0.465 psi/ft = 10.53 MPa/km). The seawater depth in this area is 248 ft (75.6m).

Least principal effective stresses (shmin = Shmin - Pp) are shown in Figure 8, separated again for sands and shales. Effective stresses show the same scatter as noted for pore pressure and Shmin in Figure 7 varying from nearly 2900 psi (20 MPa) to almost zero (in which case the sand would be expected to be close to natural hydraulic fracturing). However, the observation of larger effective stresses at greater depth for sands (Figure 8A) is counterintuitive since the gradient of pore pressure increase in the overpressured zones is generally believed to be greater than the gradient of the least principal stress, hence, reducing effective stresses. It is not surprising, therefore, that the sands with high effective stresses correlate with sub-hydrostatic pore pressure conditions being attributed to hydrocarbon production as described above. Restoration of original pore pressures and stresses will show that effective stresses prior to fluid withdrawal were lower than these

show. Although obscured by large uncertainties, the decrease in effective stress in overpressure at greater depth seems to be apparent for the shales (Figure 8B).

Figure 8: Minimum effective principal stress (shmin) vs. depth including error bars for upper and lower bounds. (A) Effective stress for sands from fracture completion reports (triangles) and LOTs (squares). (B) Minimum effective stress for overpressured (triangles) and hydrostatically pressured (squares) shales derived from leak-off tests.

Figure 9 shows the effective stress ratio, K, versus depth, for sands (Figure 9A) and for shales (Figure 9B). K is calculated by simply taking the ratio of the effective least horizontal stress shmin to the effective overburden sv (where sv = Sv - Pp):

K is used to characterize the fracture gradient as it describes the behavior of least principal stress and the overburden as a function of pore pressure. We observe on average lower K values for sands (mean = 0.54, std. dev. = 0.25) compared to shales (mean = 0.70, std. dev. = 0.33) further emphasizing a difference between lithologies in terms of pore pressure and stress.

Figure 9: Effective stress ratio K vs. depth including error bars for upper and lower bounds. Dashed line shows the effective stress ratio for Coulomb failure with a coefficient of friction of 0.6. Solid line represents a zero differential stress state. (A) K for sands from fracture completion reports (triangles) and LOTs (squares). (B) K for overpressured (triangles) and hydrostatically pressured (squares) shales.

Zoback and Healy (1984) proposed that the stress state was in frictional equilibrium

A frictional coefficient (m) of 0.6 implies a K of 0.32 (solid line in Figure 10). Neither category - sands or shales - appear to fall on this line despite the fact that sands show a distinctly lower mean value for K. Additionally, the large error bars result from the uncertainty analysis and the sensitivity of Equation 2 with respect to small changes of its parameters.

Previous studies (e.g. Brennan and Annis, 1984; Matthews and Kelly, 1967; Pilkington, 1978), have derived empirical formulas for K as a function of depth. Most of these assumed that differential stresses would eventually approach zero (e.g. K would approach 1) in overpressure at great depth. In contrast to these previous studies, our data do not show an explicit increase of K with depth. This may be due to either large uncertainties in K for both sands and shales or because of the fact that we primarily focused on data from within sands rather than shales.

Least principal stress versus pore pressure Figure 10 plot Shmin versus Pp normalized by the overburden to obtain a dimensionless plot without any explicit depth effect. The error bars denote the upper and lower bounds

for Shmin and Pp as explained in the previous section. In general, the data scatter between 0.4 and 0.95 for Pp/Sv ratios and 0.64 and 0.98 for Shmin/Sv ratios. The large uncertainties for shales in both hydrostatic and overpressured intervals are reflected by long error bars (Figure 10B). However, it is obvious that the frictional failure line for m = 0.6 marks a lower bound for most of the data. This line lies well above the hydrofracture line (when pore pressure equals the least principal stress) at low Pp, but the two lines converge as Pp increases. These observations indicate that frictional equilibrium may act as a lower bound for the least principal stress in this normal faulting environment.

Figure 10: Normalized average least principal stress vs. normalized average pore pressure. Error bars denote upper and lower bounds for pore pressures and minimum horizontal principal stresses. Also shown is the Coulomb failure line (solid) for a coefficient of friction of 0.6 and the natural hydraulic fracturing line (dashed). (A) Data for sands from fracture completion reports (triangles) and LOTs (squares). (B) Data for overpressured (triangles) and hydrostatically pressured (squares) shales. Arrows on the overpressured shale data points indicate that the absolute upper bound on these pore pressures would be the minimum horizontal stress value.

It is possible that frictional failure for m = 0.6 acts as a lower bound (Figure 11). For a fixed overburden, increased Shmin values (i.e. points above the frictional failure line for any given pore pressure in Figure 10) result in a reduction of the Mohr circle preventing Coulomb failure at m = 0.6. On the other hand, if the coefficient of friction was much lower, the sedimentary rocks would be capable of supporting only small shear stresses because of reduced strength.

Figure 11: Schematic Mohr diagram (s: effective normal stress; t: effective shear stress). Solid line illustrates the effective stress ratio of 0.32 could be a result of frictional equilibrium with m=0.6. However, most data indicate much lower differential stresses are present. Either these rocks are not at frictional failure, or the coefficient of friction is much less than 0.6.

Another way to present the data is by crossplotting K versus normalized pore pressure (Figures 12A and B). If the sedimentary rocks are in frictional equilibrium they will fall on a horizontal line independent of pore pressure. Although some data points of sands fall close to the Coulomb failure line for a coefficient of friction of 0.6 (K=0.32), neither sands nor shales (hydrostatic and overpressured) seem to directly plot onto the line. Unfortunately, the data in the figure are rather dominated by the large uncertainties as discussed earlier.

Figure 12: Effective stress ratio K vs. normalized average pore pressure. Error bars denote upper and lower bounds. Also shown is the Coulomb failure line for a coefficient of friction of 0.6. (A) Data for sands from fracture completion reports (triangles) and LOTs (squares). (B) Data for overpressured (triangles) and hydrostatically pressured (squares) shales.

Comparison with other models Comparing our results from EI-330 with several published fracture gradient compilations for the Gulf of Mexico (Figure 13) demonstrates that there is little correlation apparent either among these compilations or with our data set. The regression lines (Figure 13) were calculated at a reference depth of 6500 ft (1981m) and an average overburden gradient of 0.91904 psi/ft (20.816 MPa/km). Breckels and van Eekelen (1981) used primarily formation integrity tests (FIT) but included data from hydraulic fracturing. As can be seen from Figure 4, FIT data give essentially no indication of the least principal stress values and the fact that their FIT data match hydraulic fracturing results may not yield further constraints since the database consists of test results compiled on a regional scale being subject to large variations. Brennan and Annis (1984) relied on fracture initiation pressures from LOTs within overpressured shales. These data inherit the same problems as addressed and discussed earlier for the LOT data used in our study. Althaus (1977) correlated mud weight equivalents from circulation losses during drilling. This may also overestimate the true Shmin value depending on whether 'breakdown' of intact rock is required (Figure 4). Anderson et al. (1973) had fracture completion data available. Like our data set, these were conducted in sands and are generally comprised of high quality data. The problem with this study, however, lies in determination of pore pressures, which were derived from sonic and resistivity well log data within shale units and deterministic correlation techniques to account for Pp. Since very little is known about pore pressures in shales (generally assumed to be much higher compared with sands), this compilation inherits potential problems.

Figures 13 A-D illustrate that the individual trends of the published compilations are distinctly different from each other and also do not match our data set - neither sands nor shales. Perhaps the large variations between these examples illustrate the problem associated with purely empirical regional compilations published in the literature. Another potential problem comes from non-uniform definitions of various points on the pressure vs. time curve (Figure 4), which may provide pitfalls for interpretation of this data with respect to stress. Finally, these models are based on broad scale data compilations neglecting any heterogeneities or spatial variations in geologic structures, lithology, stratigraphy, pore pressure and stress. Hence, the results of these prove not to be useful in predicting least principal stresses for this specific Gulf Coast region of interest in this study.

Figure 13: Normalized least principal horizontal stress vs. normalized pore pressure for fracture completions and LOTs in sands (A) and LOTs within shales (B) from the EI-330 area. Also shown are different fracture gradient models: hydrofracture line, frictional failure line for a coefficient of friction of 0.6 and compilations published by Althaus (1977) (dotted line), Anderson et al. (1973) (plus symbols), Breckels and van Eekelen (1981) (dot-dashed line), and Brennan and Annis (1984) (dashed line). Reference depth for the models was 6500 ft (1981 m) and average overburden gradient was 0.91904 psi/ft (20.816 MPa/km).

Stratigraphic and structural correlations Figures 14A and 14B illustrate the stress measurement data by sand, type of measurement (squares indicate fracture completions, triangles represent LOTs), and structural location (upthrown or downthrown). Open symbols indicate a well in the downthrown block (minibasin); filled symbols indicate that the well is in the upthrown block. The first and most obvious observation is that pore pressure increases with depth. The exceptions to this (i.e. LF and OI-1 in downthrown block) result from pressure drawdown due to hydrocarbon production in these sands. A second observation is that completions in the upthrown block are in a higher pressure regime. This is because although these sands occur at shallower depths in the upthrown block, they are older and have higher shale contents than sands at similar depths in the minibasin. These include the deeper OI and L

sands, which reach fluid pressures that are 80-90% of lithostatic. These sands have higher shale contents than their overlying counterparts and are thus expected to be more highly overpressured as they are less able to expel their fluids upon burial. The KE-1 sand, with frac completions in both the upthrown and downthrown blocks, (light green) (refer to Figures 1, 2, and 3 for stratigraphic/structural position) plots remarkably close to the Coulomb failure line.

Figure 14A: Normalized least principal stress vs. normalized pore pressure for sands determined from fracture completions (squares) and LOTs (triangles). Colors mark different sand units (please refer to Figures 1, 2, and 3 for stratigraphic position). Also shown are the frictional failure line for m = 0.6 and the hydrofracture line.

The IC-4 sand (dark green) has three data points which show a slight decrease in effective stress ratio with increasing pore pressure (Figure 14B). These three completions were made in two wells (A-8ST, A-10ST) which are located close together, but have very different stratigraphic characteristics (based on wireline lithology and resistivity logs).

Unlike the fracture completion data, the LOT data (triangles) in Figures 14A and 14B indicate a definite trend of increasing effective stress ratio, K, with dimensionless pore pressure.

Figure 14B: Effective stress ratio, K, vs. normalized pore pressure for fracture completions (squares) and LOTs (triangles) in sands. Filled symbols indicate that the test was run in the upthrown block; open symbols indicate downthrown (minibasin) locations. The dashed line is the prediction of K by the Coulomb failure model, for a coefficient of friction (m) of 0.6.

Rock property correlation We attempted to correlate our stress results with rock properties by plotting effective stress ratio, K, versus porosity and vertical effective stress versus porosity (Figures 15A,B), as well as K versus percent sand of the interval (Figure 15C). Porosity data was provided in the fracture completion reports; no porosity data was available for the LOT locations. Percent sand was calculated from gamma ray logs.

Although we predict porosity to decrease exponentially with increasing vertical effective stress (following Holbrook, 1995; Hart et al., 1995), we do not see this in our data (Figure 15B). In Figure 15C, we expect to see an increase in the effective stress ratio with increased shaliness (i.e. decrease in percent sand), and although there is considerable scatter in the data (especially from the LOT points), there is somewhat of a trend of decreasing K with increasing percent sand.

Figure 15: A) Effective stress ratio (K) versus porosity for fracture completions. B) Vertical effective stress, sv, versus porosity for fracture completions (no porosity data was available for LOT locations). The filled symbols in each figure indicate an upthrown location; open symbols indicate downthrown.

Figure 15C: Effective stress ratio, K, versus percent sand for fracture completions and LOTs. Squares represent minifracs and triangles indicate LOT. As in previous figures, closed symbols indicate an upthrown location; open symbols represent downthrown wells.

Hydrocarbon production related pore pressure and stress changes Many of the fracture completions were performed after significant production had decreased the pressures from their initial state. The question arises as to what the stress behavior of the reservoir sands is during production. Does the reservoir behave poroelastically or more in a poroplastic fashion? Although it is believed that some poorly consolidated rocks may creep and dissipate most of their elastic energy over geologic timescales (e.g. Holbrook, 1995), we assume that over these short timescales during which hydrocarbons are produced, the reservoir response is elastic. We then compare this model to a location where multiple stress measurements have been made in a particular reservoir over the life of its production.

Assuming poroelastic behavior, the following formula expresses the change in horizontal stress, due to a change in pore pressure, DPp:

where n and a denote Poisson's ratio (~0.25) and Biot's coefficient (~ 1.0) respectively. This equation can be derived by differentiating the equation for total poroelastic horizontal stress under uniaxial strain conditions (Engelder and Fischer, 1994). Because the reservoir is quite broad with respect to its height, the overburden stress, Sv, does not change with pore pressure. In order to calculate the horizontal stress change with production, it is important to compare current and initial pore pressures within individual reservoirs. We plot the pressure evolution for five reservoir sands from bottom hole pressure surveys conducted following the onset of production and once a year thereafter. The drawdown has been substantial, ranging from 580 psi (4 MPa) in the KE-1 (fault block B) to 2610 psi (18 MPa) in the OI-1 (fault block C).

Figure 16A: Pressure history over 21 years of hydrocarbon production for five sands in the EI-330 minibasin. 'FB' refer to individual Fault Blocks followed by its specific ID-letter. Note, that for two reservoirs (KE-1/FBB and LF/FBB) only initial and final pore pressures were available.

For these five reservoir sands, we calculated the initial least principal horizontal stresses using Equation 3 and re-plotted them in the normalized pore pressure-stress diagram (Figure 16B). The arrows, pointing from the calculated initial values to the current observations, indicate that poroelastic reservoir behavior linearly shifts the data points approximately parallel to the frictional failure line for m = 0.6. If this model is correct, it appears as if original principal stresses in the LF and OI-1 sands had the same magnitudes (i.e. Sv = Shmin) implying almost zero strength and fluid-like deformation prior to production. Pore pressure reduction in the KE-1 sands has not been as drastic as in the other two sands over the 21 year period but the trend is nonetheless apparent.

One sand in this area was fracture completed in two different wells at different times over the course of production. The NH/FBB was completed in the B-10ST in 1992, and then in the C-18ST in 1993. These data points for the NH sand in fault block B are both included in Figures 16A and B, but not in previous figures. The two completions are located close together, both near the top of the structure, but exhibit slightly different stress and pressure characteristics. The earlier data point plots to the lower right of the latter, thus not following a path predicted by this model. It is extremely important that we obtain more multiple fracture completion data to investigate stress evolution during production.

Figure 16B: Impact of pressure drawdown on normalized average least principal stress vs. normalized average pore pressure. Solid squares show current data after approximately 20-21 years of production; open squares display initial stresses and pore pressures as calculated with Equation 3. Solid line represent Coulomb failure for m = 0.6, dashed line denotes hydraulic fracturing (Pp = Shmin).

4. Results

A. We have compared stress measurements made through leak-off tests with those made from fracture completions. Leak-off tests yield the same general trend in stress data as the fracture completion data. This is a significant finding if it will allow companies to spare the expense of the pre-frac test and use leak-off test data to determine completion parameters.

B. We have shown that sands maintain higher stress differentials than shales implying a different stress state for sands than shales.

C. We have also demonstrated a correlation of stress behavior to stratigraphic location. Different subsets of sands appear to have different stress characteristics.

5. Recommendations for Industry

A. Since our calculated overburden was significantly less than the commonly-assumed 1 psi/ft, we would recommend calculating this stress for each area of study.

B. If leak-off test data were more precisely reported it could be used in the place of pre-frac tests to assess minimum horizontal stress and pore pressure prior to fracture completion.

C. It is recommended that these data be used to define a field-specific (EI-330) fracture gradient model to be used in designing drilling programs.

6. Technical Problems and Future Work

A. A great limitation with leak-off data is that the actual pump-in data are not preserved in the daily drilling reports, so it is difficult to interpret Shmin. In addition, there were problems constraining Pp with the available information. Since it is nearly impossible to actually measure pore pressure in a shale due to the extremely low permeability, we needed to estimate the pore pressure based on porosity calculations and pressures in nearby sands. Thus, there are large uncertainties associated with stress measurements from leak-off data.

B. There are very limited stress measurements over the evolution of production, making it difficult to adequately understand the relationship between pore pressure drawdown and stress evolution.

C. It has been recommended by our industry colleagues that we distinguish between fracture completions made in 'virgin' sands (i.e. with no prior drawdown) and those made in depleted sands and that we use only 'clean' (i.e. low shale content) sands to characterize the stress field in sands.

D. A way to better understand the relationship between pressure and stress evolution would be to look for multiple fracture completions within the same sand over time. Unfortunately, fracture completions are a relatively new practice in the oil industry and these instances are therefore difficult to find. As recompletions become necessary, due to either "watering out" of downdip wells or borehole failure, it is important to analyze the pressure and stress data to understand stress evolution during production. It is critical to evaluate every instance of multiple fracture completions within the same sand.

E. Our industry colleagues were also concerned about whether or not it is possible to determine minimum horizontal stress in deviated boreholes due to near-borehole effects (i.e. since hoop stress effect is highly dependent on borehole orientation.

F. Some of the scatter in the data may be eliminated by observing the in situ pressures measured in surge tests immediately following perforation.

G. Diffusive fluid loss is a major problem in determining leak-off values. These errors in data can be reduced by increasing the pumping rate in cases where diffusive fluid losses may be present.

H. A different contractor performed D-platform completions. We need to be sure that this second group followed similar methods of interpretation before we can accurately compare results.

I. There are alternative methods to predicting porosity in shales. We are currently comparing these alternative methods to the approach used in this report.

7. Conclusions

Analysis of fracture completion reports from various reservoir sands and LOT data from shales within and adjacent to a typical Gulf Coast minibasin show considerable variations in pore pressure and least principal stress values. Pore pressures range from sub-hydrostatic to nearly lithostatic which also controls variations in Shmin magnitudes and hence effective stress. Sub-hydrostatic pore pressures correlate with reservoirs of high pore pressure changes due to fluid production.

Effective stress ratios (K) are on average smaller for sands than for shales, implying a difference between lithologies in terms of least horizontal stress as a function of pore pressure and overburden. However, large uncertainties accompany the data and a correlation with frictional failure for a coefficient of friction of 0.6 (i.e. stress ratio, K, of 0.32) was not found. Generally, the Coulomb failure model, using a frictional coefficient of 0.6, underpredicts the effective stress ratios calculated in this study.

Comparison with previously published compilations of fracture gradients in the Gulf Coast regions shows significant differences between the various models and our data set. This most likely reveals large variations in both rock behavior and data quality implying potential problems with applying generalized models developed by previous authors to the Gulf Coast region as a whole - especially when considering the large uncertainties that accompany most data sets and are often neglected.

Stratigraphic position and composition may have significant effects on the stress state of a sand interval. Pressure and stress vary greatly between sands. Also, although there is some scatter in the data, the effective stress ratio, K, appears to increase with increased shale content.

Production history data are used to document a pressure decline. When a poroelastic model is used to restore stresses to their original values, we observe that hydrocarbon production and fluid pressure reduction moves data points along a line approximately parallel to the frictional failure line for a coefficient of friction of m=0.6. Our limited data of multiple fracture completions over time, from the NH sand, do not appear to follow this modeled behavior.

8. Acknowledgments

We would like to thank Pennzoil, Shell, and Texaco for generously providing the data used in this analysis.

9. Nomenclature

10. References

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11. Appendix

We have compiled three tables that show the data used in this study. Table A1 contains information from the fracture completions, Table A2 shows LOTs carried out in sands, and Table A3 are the LOTs within shale units - hydrostatically pressured and overpressured. All three tables display well name, subsea true vertical depth (SSTVD), spatial location of test in Lambert coordinates, name of the sand or the nearest sand in case of shale layers, lower and upper pore pressure bounds and the calculated errors, lower and upper least horizontal stress bounds and their errors, the overburden stress including its uncertainty, and finally normalized pore pressure and least horizontal stress accompanied by their errors as well. Pressure and stress terms are in psi and depths are in feet.