Abstract

Repeated pressure measurements undertaken throughout the depletion of oil fields demonstrate that reduction in pore pressure is accompanied by a reduction in total minimum horizontal stress (σh), a phenomenon described herein as oil field-scale pore pressure/stress (Pph) coupling. Virgin pressure measurements (i.e. those unaffected by depletion) through normally and overpressured sequences in sedimentary basins demonstrate that overpressure development is accompanied by an increase in σh, described herein as sedimentary basin-scale Pph coupling. With depletion of the Ekofisk Field, North Sea, minimum horizontal stress decreased at approximately 80% of the rate of reduction of reservoir pore pressure (i.e. ΔσhPp≈0.8). Virgin pressures measured in exploration wells surrounding the Ekofisk Field (Norwegian quadrants 1 and 2) indicate that with overpressure development ΔσhPp≈0.73 (assuming shallow, normally pressured sequences are representative of overpressured sequences prior to overpressure development). Hence, despite the different temporal and spatial scales, the rate of decrease of minimum horizontal stress with pore pressure due to depletion of the Ekofisk Field is similar to the rate of increase of minimum horizontal stress with pore pressure due to overpressure development in the surrounding region. Basin-scale exploration pressure data in the Ekofisk region may thus provide an indication of the reservoir stress changes associated with depletion. Knowledge of such stress changes is critical because they can lead to the collapse of uncased wellbores, sand production and to faulting/fracturing and seismicity with field development.

Introduction

Repeated stress measurements in a number of oil fields have revealed that there is a reduction in the total minimum horizontal stress (σh) during the life of a field, as the reservoir is depleted and pore pressure (Pp) reduces (Salz 1977; Whitehead et al. 1987; Teufel et al. 1991; Fig. 1). The reduction in minimum horizontal stress that accompanies reducing pore pressure is known as the reservoir stress path (Santarelli et al. 1998; Khan & Teufel 2000). In sedimentary basins, measurements of virgin pressures (i.e. those unaffected by depletion) indicate that minimum horizontal stress increases from shallow, normally pressured sequences into deeper, overpressured sequences, over and above that due to increasing depth (Bell 1990a; Gaarenstroom et al. 1993; Yassir & Bell 1994; Fig. 2). The changes in minimum horizontal stress that accompany changes in pore pressure are herein termed pore pressure/ stress (Pph) coupling. The relatively rapid and localized reduction in minimum horizontal stress that accompanies pore pressure reduction associated with field depletion is termed oil field-scale Pph coupling, and the increase in minimum horizontal stress developed over geological timescales in regional pressure compartments in association with increasing pore pressure is termed sedimentary basin-scale Pph coupling.

The nature of Pph coupling is critical to both oil field development and sedimentary basin tectonics. Stress changes caused by reservoir depletion in an oil field impact on the stability of open (uncased) wellbores throughout the life of the field (Addis 1997), on sand production and on faulting/ fracturing and seismicity associated with reservoir depletion and flooding (Teufel et al. 1991; Segall & Fitzgerald 1998). At the basin scale, the nature of coupling determines the limits to overpressure that can be sustained prior to rock failure and the mode (shear versus tensile) of that failure (Lorenz et al. 1991) and, thus, for example, the occurrence of shale diapirism/mud volcanoes (Morley et al. 1998).

Clear distinction has not always been made between depletion-related Pph coupling at the oil field scale, and overpressure-related Pph coupling at the sedimentary basin scale. For example, Breckels & van Eekelen (1982) determined the rate of change of minimum horizontal stress with pore pressure combining both field- and basin-scale data, thereby implicitly assuming naturally overpressured and anthropogenically depleted pore pressures exhibit similar ΔσhPp values. Addis (1997) distinguished field- and basin-scale data, suggesting that minimum horizontal stress acting in reservoirs due to natural variations in pore pressure may be useful in estimating the likely reaction of a reservoir undergoing depletion, though he suggested that the basin-scale data may represent a near-equilibrium value, compared to the more transient responses at the field scale. Khan & Teufel (2000) suggested that the stress relationship is essentially the same for production-induced or geologically induced changes in pore pressure. If, indeed, ΔσhPp is similar at the field and basin scale, then virgin, exploration-derived stress and pressure data may be useful in making predictions of the stress drop that will accompany the reduction of reservoir pressure with production, thereby facilitating reservoir development planning.

Oil field- and sedimentary basin-scale Pph data for the same region have not been previously explicitly compared. The main purpose of this paper is to investigate, using previously published data from the Ekofisk Field (Teufel et al. 1991) and new exploration pressure data from the surrounding region, whether ΔσhPp is similar at the field and basin scale and, thus, whether basin-scale data may be used to help predict field-scale changes. This paper also compares and contrasts field- and basin-scale Pph coupling and discusses their implications for oil field development and sedimentary basin tectonics.

Relations Between Pore Pressure and Stress

Since being introduced by Matthews & Kelly (1967), the ratio (k) of the minimum horizontal effective stress (σhPp) to the vertical effective stress (σvPp) has been commonly used to describe the state-of-stress in the sub-surface:

 

k=σhPpσvPp.

Rearranging Equation (1) yields:

 

σh=k(σvPp)+Pp

or

 

σh=kσv+(1k)Pp,

the former of which is equivalent to the standard fracture gradient relation (Traugott 1997). Considering changes in pore pressure and minimum horizontal stress with time, and assuming that the vertical stress is constant (weight of overburden), Equation (3) yields:

 

ΔσhΔPp=1k

There have been a number of different approaches to determining the constant k. In the context of field depletion, k has been most widely determined based on the poroelastic response of rocks under uniaxial strain conditions, i.e. no lateral expansion (e.g. Santarelli et al. 1998; Segall & Fitzgerald 1998; Khan & Teufel 2000), whereby:

 

k=v1v,

where νis Poisson’s ratio. This approach has also been used to describe basin-scale Pph coupling (Engelder & Fischer 1994; Addis 1997). In Holbrook’s (1997) solidity approach, the constant k is given by the complement of porosity, i.e. solidity. Alternatively, if the sediment deforms in the plastic domain, k=1 (Santarelli et al. 1998; Schneider et al. 1999). Finally, the constant k can be determined based on the assumption that rock stresses are in equilibrium with those required to induce frictional failure (Jaeger & Cook 1979; Zoback & Healy 1984). Assuming that there exist suitably orientated planes of no cohesion, and a normal fault regime typical of passively subsiding sedimentary basins:

 

k=1{(μ2+1)+μ}2,

where μ is the coefficient of rock friction. In Equations (1–4), Biot’s poroelastic constant (a) has been assumed to be unity, as is commonly the case. However, the above can easily be adapted to cases where a is not unity by replacing Pp with aPp and ΔPp with aΔ Pp.

Herein k is considered a constant calibrated by measured pressure data. The extent to which k relates to Poisson’s ratio, solidity, the coefficient of rock friction, or indeed is equal to one, depends on the extent to which the assumptions in the various models are satisfied. It is not the purpose of this paper to discuss these assumptions. However, the assumptions are not likely to be fully satisfied in any of the models, hence, as suggested by Mouchet & Mitchell (1989), values for k determined by calibration to measured pressure data should not be considered to yield the physical properties pertaining to the different models. The empirical approach favoured herein has been widely followed (e.g. Breckels & van Eekelen 1982).

Engelder & Fischer (1994) argued that pore pressure and minimum horizontal stress data from the UK North Sea and Canadian Scotian Shelf were consistent with the poroelastic model, but not with the frictional failure model. However, as pointed out by Zoback et al. (1995), the predictions of frictional failure do indeed also fit these data, as could the predictions of Holbrook’s (1997) solidity model. Given that all these models result in the relations presented in Equations (1–4), they cannot be differentiated based on how well they fit measured pressure data in a normal fault regime basin. Herein it is simply noted that provided k is less than one, the models predict that changes in pore pressure should be accompanied by changes in minimum horizontal stress. It is also noted that none of the models explicitly take account of the different temporal and spatial scales of Pph coupling at the oil field and sedimentary basin scales.

PPH Coupling at the Oil Field and Sedimentary Basin Scales

Comparing and contrasting field and basin scales

The reduction in minimum horizontal stress that accompanies a reduction in pore pressure due to reservoir depletion (oil field-scale Pph coupling) has been demonstrated in the Oligocene Vicksburg Formation of south Texas (Salz 1977), the Eocene C4 and C5 sands of the Lake Maracaibo region of Venezuela (Breckels & van Eekelen 1982), the Cretaceous Travis Peak Formation in east Texas (Whitehead et al. 1987) and the Danian–Maastrichtian Chalk of the Ekofisk Field, North Sea (Teufel et al. 1991). Addis (1997) summarized these examples and presented additional data illustrating field-scale Pph coupling from the Magnus Field (Northern North Sea), West Sole Field (Southern North Sea) and Wytch Farm Field (southern UK). Santarelli et al. (1998) presented data from an unnamed North Sea field where different parts of the field displayed different rates of decrease of minimum horizontal stress with pore pressure.

An increase in minimum horizontal stress from shallow, normally pressured sequences into deeper, overpressured sequences, over and above that due to increasing depth (sedimentary basin-scale Pph coupling), has been demonstrated by virgin pressure measurements (i.e. those unaffected by depletion) in the Scotian Shelf offshore eastern Canada (Ervine & Bell 1987; Bell 1990a; Yassir & Bell 1994) and in the Central North Sea (Gaarenstroom et al. 1993). Coupling between pore pressure and minimum horizontal stress has also been demonstrated in the US Gulf Coast and in Brunei, for which Breckels & van Eekelen (1982) presented field- and basin-scale data.

Sedimentary basin-scale data, unlike oil field-scale data, do not provide a priori evidence of Pph coupling, because changes in pore pressure and minimum horizontal stress with time cannot be demonstrated. However, if it is assumed that shallow, normally pressured sequences are representative of the overpressured sequences prior to overpressure development, then the nature of basin-scale Pph coupling may be inferred (Fig. 3). This assumption is analogous to that made in basin modelling where present-day porosity–depth or porosity–effective vertical stress relations are used to describe the porosity evolution of a sediment with progressive burial.

Repeated pressure measurements in an oil field are obtained at approximately the same (reservoir) depth, hence the requirement in Equation (4) that vertical stress is constant is satisfied and coupling effects can be demonstrated by plotting pore pressure and minimum horizontal stress directly against one another (Fig. 3e). However, sedimentary basin-scale data are collected over a range of depths and the relationship between pore pressure and minimum horizontal stress in basin-scale data primarily reflects the increase with depth exhibited by both (Fig. 3b). Hence, it is necessary to depth-normalize basin-scale data, as pressure gradients, in order to compare them with field-scale data on Pph coupling (Fig. 3c). Expressing Equations (2) in terms of pressure gradients with respect to depth (z):

 

σhZ=kZ(σvPp)+PpZ.

Similarly, assuming shallow, normally pressured sequences are representative of overpressured sequences prior to overpres-sure development, Equation (4) can be re-written in terms of changes in pressure gradients with time for basin-scale data:

 

ΔσhZΔPpZ=1k

Equation (8) assumes that the vertical stress gradient is constant (cf. Equation (4) which assumes that the vertical stress is constant). In order to facilitate comparison, field-scale data can also be depth-normalized (Fig. 3f). Breckels & van Eekelen (1982) and Addis (1997), who presented both field- and basin-scale data, depth-normalized their basin-scale data. However, Amundsen (1995) did not, and the Pph relationship presented therein primarily reflects the increase with depth exhibited by both pore pressure and minimum horizontal stress.

In addition to sampling a range of depths, basin-scale data also sample a wide range of lithologies, unlike field-scale data which are generally restricted to a reservoir interval that exhibits much less lithological variation. Hence, even if the processes controlling coupling at the oil field and sedimentary basin scales are similar, basin-scale Pph data might be expected to display greater scatter than field-scale data, because of the wider range of physical properties sampled (e.g. Poisson’s ratio, porosity and the coeffcient of rock friction). The timescale of Pph coupling at the oil field and sedimentary basin scale provides an additional, potentially significant difference between the two scenarios. Oil field-scale Pph coupling is associated with depletion of reservoir pore pressure over the years to tens-of-years period of field development, whereas sedimentary basin-scale Pph coupling associated with overpressure development is developed and maintained over geological timescales. The differences in the spatial and temporal scales of oil field- and sedimentary basin-scale Pph coupling beg the questions as to whether the same processes control Pph coupling in the two scenarios and, more pragmatically, whether the rate of change of minimum horizontal stress with pore pressure (ΔσhPp) is similar at the field and basin scale. Herein, Teufel et al.’s (1991) Ekofisk Field data are compared with virgin, basin-scale pressure measurements (i.e. those unaffected by depletion) from the surrounding area.

Data sources

The most reliable determinations of minimum horizontal stress are yielded by hydraulic fracture tests. In such tests a tensile fracture is opened by increasing the fluid pressure within an isolated section of wellbore. The fluid pressure at which the hydraulic fracture closes provides a direct estimate of σh, based on the assumption that the fluid is holding the fracture open against the least principal stress (see Engelder 1993 for a review of the procedure). Teufel et al.’s (1991) minimum horizontal stress data from the Ekofisk Field were based on such hydraulic fracture-type tests which are often undertaken as part of hydraulic fracture stimulation treatments in low permeability reservoirs. Unfortunately, hydraulic fracture tests are not widely undertaken during exploration drilling. However, leak-off tests, in which the pressure at which a fracture opens is determined, are routinely undertaken. Such leak-off (or fracture) pressures are routinely determined because they give an indication of the maximum mud weight that can be used without generating fractures into which drilling mud would be lost while drilling ahead. Leak-off pressures do not yield as reliable estimates of minimum horizontal stress as fracture closure pressures, largely because the leak-off pressure is controlled by the disturbed stress field at the wellbore wall, and because the leak-off pressure must overcome any tensile strength of the formation. None the less, it is widely accepted that the lower bound to leak-off pressures gives a reasonable estimate of minimum horizontal stress (Breckels & van Eekelen 1982; Bell 1990b; Gaarenstroom et al. 1993; Engelder & Fischer 1994). Herein leak-off pressures are used as a proxy for minimum horizontal stress in the exploration (basin-scale) data.

Direct pressure measurements from hydraulic fracture tests, formation tests or drill stem tests provide the most reliable determination of pore pressures. These are often available for field data such as for Teufel et al.’s (1991) Ekofisk data, but are not generally available at the same depth as the leak-off tests in basin-scale (exploration) data. Mud pressures in the open hole are generally kept slightly in excess of formation pore pressures to prevent the entry of formation fluids into the wellbore. Mud pressures are invariably raised when elevated pore pressures are encountered and hence reflect overpressure. Mud pressures may be increased for reasons other than elevated pore pressures (e.g. to maintain wellbore stability) but, in general, mud pressures significantly higher than formation pore pressure are avoided because of the resultant reduced rate of penetration, additional mud costs and potential for formation damage. Given that the transition zones from normally to overpressured intervals may be narrow (Swarbrick & Osborne 1996), the disadvantages of using depth-offset direct pressure measurements to analyse Pph coupling at the basin scale are considered greater than those of using mudweights at the depth of the leak-off test.

Ekofisk region of the North Sea

The Ekofisk Field is located in the southern part of the Norwegian sector of the North Sea (Fig. 4). In response to the drawdown in reservoir pressure in the crestal area of the field from approximately 45 MPa in 1975 to 25 MPa in 1990, minimum horizontal stress decreased from approximately 51 MPa to 35 MPa (Fig. 1; Teufel et al. 1991). The flanks of the field have been subject to a comparable, coupled decrease in pore pressure and minimum horizontal stress (Fig. 1). In order to compare these field-scale data with basin-scale data from the surrounding area, the field-scale data presented by Teufel et al. (1991) have been converted to pressure gradients, taking the depth of the crest of the Ekofisk Field as 2.9 km, the flanks as 3.0 km and the outer flanks as 3.1 km (Fig. 5).

Leak-off pressure gradients (avoiding limit-type formation integrity tests) and mud pressure gradients have been compiled for exploration wells in Norwegian quadrants 1 and 2 within approximately 50 km of the Ekofisk Field (Figs 4 and 5). The wells were filtered to exclude any in which production might have resulted in depletion effects (G. Caillet pers. comm. 1997).

Given the different spatial scales over which oil field- and sedimentary basin-scale data are sampled, the different time-scales by which they are influenced, and the different methods of determining pore pressure and minimum horizontal stress, there is a high degree of consistency between the two datasets from the Ekofisk region (Fig. 5). Teufel et al.’s (1991) data from the Ekofisk Field (Fig. 1) are consistent with a Δσh/Δ;Pp coupling ratio of 0.8, i.e. k=0.2. A linear regression of the virgin pressures from the basin-scale exploration wells yields a ΔσhPp coupling ratio of 0.73, i.e. k=0.27. The field- and basin-scale data both lie on a similar trend, although there is a tendency for basin-scale minimum horizontal stress to be somewhat greater than the field scale at the same pore pressure. This is consistent with the fact that the field-scale minimum horizontal stress data are based on hydraulic fracture tests, whereas the basin-scale data are based on leak-off pressures, the lower bound to which gives a reasonable estimate of minimum horizontal stress.

Discussion

In the Ekofisk example discussed above, the sedimentary basin-scale ΔσhPp coupling ratio witnessed by virgin, exploration pressures (i.e. those unaffected by depletion) from shallow, normally pressured sequences into deeper, overpressured sequences, is broadly consistent with the oil field-scale ΔσhPp coupling ratio observed in a reservoir over fifteen years of field production. Hence, the nature of Pph coupling apparent from exploration data may provide valuable input into assessing whether changes in the state-of-stress associated with hydrocarbon production are likely to lead to wellbore instability or faulting/fracturing and seismicity. The prediction of such effects is becoming increasingly important as the oil industry investigates reservoirs such as the high pressure–high temperature gas condensate fields of the Central North Sea which will undergo depletion of 40–80 MPa (Addis 1997; Santarelli et al. 1998).

The increase in effective stress associated with reservoir depletion and pore pressure reduction would reduce the propensity for faulting and seismicity if differential stress remained constant (Fig. 6a). However, total vertical stress (σv), which is given by the weight of the overburden, is unaffected by changes in pore pressure (Teufel et al. 1991; Engelder 1993). Hence, effective vertical stress (σvPp) increases at the rate that pore pressure decreases. Effective horizontal stress (σhPp) increases more slowly than pore pressure decreases (or effective vertical stress increases) because total horizontal stress decreases with pore pressure (Fig. 6b). Hence, in a normal fault regime sedimentary basin (σvHh), Pph coupling leads to an increase in differential stress (σ1–σ3, here σv–σh) with reducing pore pressure and may result in depletion-related rock failure (Teufel et al. 1991). An ability to predict the ΔσhPp coupling ratio prior to field development is a critical aspect of predicting the occurrence of faulting/fracturing and seismicity during field development. Furthermore, assessment of the stability of uncased wellbores through reservoir depletion must also incorporate predictions of the ΔσhPp coupling ratio (Addis 1997). The Ekofisk data suggest that virgin, exploration pressures from shallow, normally pressured sequences into deeper, overpressured sequences, may be useful in helping constrain such changes.

It is not the contention herein that sedimentary basin-scale σh/Pp data will always successfully predict oil field-scale changes. It is clear from Salz’s (1977) McAllen Ranch, south Texas data that there is significant heterogeneity within reservoirs (ΔσhPp varies from 0.37 to 0.62 in the six intervals). Similarly, Santarelli et al. (1998) described an unnamed reservoir in the Norwegian North Sea within which the ΔσhPp coupling ratio varied from 0.70 to 0.42 in a part of the field more obviously affected by seismic-scale faults. Clearly the basin-scale data cannot reflect heterogeneities at the intra-field-scale, and can only be used as a broad indicator of likely behaviour with depletion. Furthermore, Khan & Teufel’s (2000) modelling results indicate that the ΔσhPp ratio depends on the size and geometry of the reservoir and on the elastic properties of the reservoir rock and bounding formations. The ΔσhPp ratio increases as the aspect ratio (length/ thickness) increases, lenticular sands having a lower ratio than blanket sands.

The implications of Pph coupling at the sedimentary basin-scale have not been widely recognized. Pph coupling effects are significant both to the amount of overpressure that can be sustained before rock failure, and the nature (shear versus tensile) of failure that results. The limit to overpressure provided by tensile failure (σ3Pp<T ) is widely taken to imply that pore pressure can only increase by the difference between prevailing Pp and σh, assuming σ3h and T=0 (e.g. Du Rouchet 1981; Watts 1987; Gaarenstroom et al. 1993). However, because effective horizontal stress (σhPp) decreases more slowly than pore pressure increases, the limit to overpressure is significantly greater than the difference between prevailing pore pressure and minimum horizontal stress (Fig. 6c). In order for tensile failure to occur, pore pressure must increase by a factor {1/(1–ΔσhPp)} greater than predicted if it is assumed that minimum horizontal stress is unaffected by pore pressure, i.e. pore pressure must increase 3.7 times greater than the difference between prevailing pore pressure and minimum horizontal stress for failure to occur assuming the basin-scale ΔσhPp ratio of 0.73 for the Ekofisk region. In overpressured provinces it is commonly assumed that the maximum hydrocarbon column height that can be trapped is one that generates a buoyancy pressure equal to the difference between the prevailing pore pressure and minimum horizontal stress (e.g. Caillet 1993; Gaarenstroom et al. 1993). However, if stresses respond similarly to the buoyancy pressure of hydrocarbon columns as to overpressure, then significantly larger columns may be trapped.

Effective horizontal stress (σhPp) decreases more slowly than pore pressure increases (or effective vertical stress decreases) because total horizontal stress decreases with pore pressure. Hence, considering a normal fault regime basin, the diameter of Mohr’s circle reduces as overpressure develops (Fig. 6c). This reduction of differential stress as pore pressure increases promotes tensile over shear failure as the mode of overpressure-induced rock failure.

Conclusions

Changes in pore pressure and minimum horizontal stress are coupled both at the anthropogenic timescale of the depletion of oil fields, and at the geological timescale of the development of overpressure in sedimentary basins. In the Ekofisk region of the North Sea the ΔσhPp coupling ratio is similar at both the oil field and sedimentary basin scale, despite differences in the spatial and temporal scale of coupling at the field and basin scale, and in the different types of pressure data available with which to analyse it in these two scenarios. Hence, in the absence of other data, virgin, exploration pressures (i.e. those unaffected by depletion) may be used to indicate the likely nature of minimum horizontal stress changes as a field is produced and the reservoir pressures drawn down. At the local scale, reservoirs are likely to exhibit heterogeneity that is not observed within the basin-scale data. None the less, especially in basins where there is little production history, or monitoring of depletion-related Pph coupling, basin-scale data may provide a valuable input to prediction of depletion-related changes in the state-of-stress.

Oil field-scale Pph coupling controls whether faulting/ fracturing and seismicity accompanies depletion and must also be factored into the assessment of the stability of uncased wellbores throughout field development (Fig. 6b). As a result of sedimentary basin-scale Pph coupling, more overpressure can be sustained in overpressured compartments prior to rock failure than is predicted by uncoupled models of rock failure, and the reduction of differential stress as pore pressure increases promotes tensile over shear failure with overpressure development (Fig. 6c).

Unfortunately there are no data known to the author on the nature of changes in maximum horizontal stress with pore pressure at either the oil field or sedimentary basin scale. Hence, the behaviour of the full stress tensor with changes in pore pressure remains unconstrained. In order that the above issues pertinent to both oil field development and sedimentary basin tectonics may be more fully addressed, it is necessary to improve our understanding of the way in which maximum horizontal stress varies with pore pressure at the oil field and sedimentary basin scale.

Gerard Caillet of Elf Petroleum Norge is thanked for virgin, exploration pressure data from the area surrounding the Ekofisk Field. Dick Swarbrick (Durham University) is thanked for discussion of the concepts presented in this manuscript. Frédéric Schneider and Alain Mascle are thanked for their constructive reviews of the manuscript. This work has been carried out in participation with the Australian Petroleum Cooperative Research Centre (APCRC) Pore Pressure Programme.