INTRODUCTION

Many major sedimentary basins in the world are known to contain fluid pressures significantly in excess of hydrostatic pressure. This condition is known by various names: "geopressure," "excess pressure," "overpressure," or "abnormally high" pore pressure. Within the United States, the classic example of such a situation occurs in the Gulf Coast sedimentary basin. The South Caspian basin in the USSR also contains high pore pressures, which are the subject of this paper.

Several investigations have discussed the processes that can generate high pore pressures (e.g., Tkhostov, 1963; Powers, 1967; Bredehoeft and Hanshaw, 1968; Burst, 1969; Smith, 1971; Barker, 1972; Durmyshyan, 1973a; Magara, 1975; Dobrynin and Serebryakov, 1978, Buryakovsky et al, 1983). Mathematical models of varying complexity have been applied in an attempt to explain the overpressures; these include studies by Bredehoeft and Hanshaw (1968), Smith (1971, 1973), Sharp and Domenico (1976), Dobrynin and Serebryakov (1978), Bishop (1979), Keith and Rimstidt (1985), and Bethke (1986b). These models focused on the idealized situation of pore-pressure development within a homogeneous, laterally extensive, shale sequence. Sand bodies were either not included in the analysis or were consider d to be isolated lenses within the shale body. Flow within the system was assumed to be vertical, normal to the bedding.

Several authors, Harkins and Baugher (1969), Chapman (1972, 1973, 1983), and Magara (1976), have indicated that lateral flow of formation fluids within the sands in a layered sand-shale sequence could be an important component of the compaction process. Bethke (1986, 1986a) examined the problem of compaction-driven fluid flow within intracratonic basins. Bethke implicitly incorporated sands in his numerical models, which indicated that compaction can drive lateral fluid flow in a subsiding basin. Walder (1984) explicitly examined the problem of lateral fluid flow within the sand layers in a basin in which overpressures exist. Walder argued on a purely theoretical basis that lateral flow within the sand layers may be important; unfortunately, he had no empirical data to substantiate hi argument.

In this paper, we examine pore pressures in the South Caspian basin, where lateral flow within the sand layers is, we believe, an important component of the compaction process. To our knowledge, we are the first to have sufficient empirical data to indicate that lateral flow on a regional scale is occurring within the sands in an actively subsiding basin with substantial overpressures. We have attempted a first-order mathematical analysis of pore pressures within the basin in an effort to show that this hypothesis is reasonable. Although our analysis differs from that of Walder (1984), our mathematical model and many of our assumptions are similar to his.

SOUTH CASPIAN BASIN

The South Caspian sedimentary basin is situated beneath the southern half of the Caspian Sea (Figure 1). Although most of the sedimentary basin is beneath the sea, small areas exist on land both to the east in the Turkmenian

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SSR and to the west in the Azerbaijan SSR. The basin is filled with Cenozoic clastic sediments that overlie a Mesozoic complex of volcanic and sedimentary rocks (Figure 2).

The area of particular interest in this paper is in the northwestern part of the South Caspian basin in the vicinity of the Baku Archipelago (Figure 3). This portion of the basin is an area with numerous oil and gas fields, and is the focus of continuing exploration, especially offshore beneath the Caspian Sea.

The South Caspian basin is characterized by high rates of Cenozoic sedimentation; in some places the rate is 1,300 m/m.y. The basin contains an enormous thickness of sediments, approximately 25 km in the deepest parts. Abnormally high pore pressures exist in some areas; the average pore-pressure gradient is 0.018 MPa/m (0.78 psi/ft) (Figure 4). The basin is also characterized by a low geothermal gradient (16°C/km); temperatures at a 6-km depth do not exceed 110°C. Within the basin occur more than 400 known mud volcanoes (Figure 5).

Within the northwestern part of the basin, sand and shale are the predominant lithologies. Within the shales, the clay minerals constitute approximately 70% of the solids present; montmorillonite and illite usually account for 70-80% of the clay minerals. The ratio of montmorillonite to illite is approximately equal. Kheizov (1979) and Buryakovsky et al (1983), in studies of clay minerals, pointed out that no discernible change takes place in the ratio of montmorillonite to illite to a depth of 6,000 m. However, in the Gulf Coast of the United States a transformation of montmorillonite to illite occurs at a depth below 1,800 m (Burst, 1969; Perry and Hower, 1970; Weaver and Beck, 1971). The presence of montmorillonite at such great depths is explained by Djevanshir (1985a, b) as due t low temperatures, high pore pressures, and low salinity of the formation waters.

We have subdivided the northwestern part of the basin into three areas for the purpose of analysis. Each area has a different ratio of sand to shale as indicated in Table 1 and has a different pore-pressure regime, as discussed below. In addition, the sedimentary sequence varies from area to area as shown by the data on average shale-bed thicknesses.

Fig. 1. Location map showing approximate boundary of the South Caspian sedimentary basin. Cross section AA^prime is shown in Figure 2. Rectangular region outlined in vicinity of Baku is shown in Figure 3.

Fig. 2. South-north cross section AA^prime shows generalized stratigraphy of South Caspian sedimentary basin (from Shikhalibeyli et al, 1984). Dashed lines show possible fault cutting Cenozoic and upper Mesozoic.

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PORE PRESSURE

Each of the three areas identified on Figure 3 has a different pore-pressure regime. Plots of the pore-pressure head vs. depth for both sands and shales are shown in Figure 4 for areas I, II, and III. Data for pore-pressures within the shales were determined from analyses of geophysical well logs, using a method given by Dobrynin and Serebryakov (1978). This method is analogous to the technique described by Hottman and Johnson (1965). Data for pore pressures within the sands were obtained from bottom-hole pressure measurements. Data for sands are not as numerous as those for shale. In many places, the pore pressure in the sands has been disturbed by earlier hydrocarbon production and must be extrapolated to virgin conditions. In extrapolating the data, the data for pressure vs. time a e plotted and an extrapolation to infinite time is made. Such extrapolations produce estimates, which if they are in error, tend usually to be too high rather than too low.

Area I:
The pore pressure in the shale is 1.2 times hydrostatic. Within the sands, the pore pressure is approximately hydrostatic, especially below 3,000 m.

Area II:
The pore pressure in the shale is approximately 1.5 times hydrostatic. Pore pressure within the sands is lower than the shales, approximately 1.2 times hydrostatic.

Area III:
The pore pressure in the shale is approximately 1.8 times hydrostatic. Within the sands, pore pressure is again lower than in shale, approximately 1.4 times hydrostatic.

The hydraulic head within the sands is plotted at various depths in Figure 6. In order to plot Figure 6, we have fit a line through the pressure depth data for each of the three areas. Because the datum for defining hydraulic head is arbitrary, we have taken the level of the Caspian Sea as our reference. The usual definition of "excess" hydraulic head is "head above the land surface"; the heads portrayed in Figure 6 are, therefore, excess head.

Several trends are striking in the pore pressure data. (1) The sands in all three areas have pressures substantially below those that exist within the shales. An exception to this generalization occurs in area III where a number of the pressure determinations in sand at a depth of approximately 1 km approach lithostatic pressure (Figure 4). (2) A regional pore-pressure gradient exists within the sands with head decreasing from area III to area II toward area

Fig. 3. Area of investigation near the Baku Archipelago (Apsheron Peninsula) (marked by rectangle on Figure 1). Areas I, II, and III show differing sand-shale ratios (Table 1) and pore-pressure regimes.

Fig. 4. Pore pressure vs. depth for both shales and sands in areas I, II, and III.

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I. (3) The distribution of pore pressure vs. depth seems to be approximately linear in both the sand and the shale to a depth of 5 km in all areas. (4) A substantial upward, vertical head gradient occurs in areas II and III.

The data, we believe, indicate that the sands are acting as drains for the compacting shales. Fluids expelled from the shales during compaction move vertically through the shales into the sands and then migrate laterally in the sands.

ANALYSIS OF REGIONAL SAND PERMEABILITY

The hypothesis that the interbedded sands are acting as drains on a regional scale for fluids being expelled from the compacting shales can be tested by calculating the regional permeability of the sands necessary to produce the observed excess hydraulic head. In the following sections, a first-order mathematical analysis is used to calculate values of regional sand permeability in the South Caspian basin. The objective of such a first-order analysis is to evaluate the reasonableness of our hypothesis. The results serve only to test the thesis that the sands act as regional drains for the compacting shales.

SHALE POROSITY

Calculation of regional sand permeability requires estimating the rate of fluid production from the compacting shales. We used observed porosity-depth relationships to make estimates of the rates of compaction (i.e., fluid production). Numerous laboratory determinations of shale porosity have been made from cores of shale taken from the three areas of interest (Durmyshian, 1973b). A summary of the shale porosity vs. depth data is presented in Table 2 and plotted in Figure 7.

The relationship of porosity vs. depth has been the subject of numerous studies. In many studies, the porosity vs. depth function is chosen to be some form of exponential relationship (see Rieke and Chilingarian, 1974). Athy (1930) was the first to propose an exponential relationship, which is sometimes referred to as "Athy's law."

We have made a least-squares fit of an exponential function to the porosity-depth data:

EQUATION (1)

where ^phgr = porosity, a and b = constants, and z = depth. The fits of the exponential curves to the data are shown on Figure 7. In fitting the exponential functions, we have forced the porosity at the surface to be 40%. As can be seen, the fit for area I appears to be quite good. In areas II and III, a number of the shallower data points fall above the fitted exponential curves. Forcing a common 40% porosity at the surface significantly degrades fit in area II and especially in area III.

In order to make our analysis, we further assumed that (1) the rate of subsidence is constant, (2) the porosity vs. depth relationship is stable with time at any given location within the basin, and (3) the sediment-water interface remains at z = 0. These assumptions are illustrated schematically in Figure 8.

The total change in porosity (^Phgr) at any point within the basin is given by the substantial derivative, and is

EQUATION (2)

If equation 2 is evaluated at a constant depth and if we assume that the porosity vs. depth relationship at any one location is more or less stable with time (i.e., D^phgr/Dt = 0), then the change in shale porosity with time is given by

EQUATION (3)

Fig. 5. Location map of prominent mud volcanoes in South Caspian basin (from Dadashev and Guliev, 1984).

Table 1. Shale Thickness Data for Three Areas in South Caspian Basin

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The rate of compaction (^dgrv^phgr/^dgrvt), and thus fluid production, can be related to the porosity vs. depth profile (^dgrv^phgr/^dgrvz) and to the upward velocity required to remain at a constant depth (^dgrvz/^dgrvt). The required upward velocity at any given point in the profile will be the negative of the rate of subsidence at that point. As a first-order approximation, we assume that ^dgrvz/^dgrvt = -r_s where r_s is the rate of near-surface subsidence. This expression is only approximate, as the rate of subsidence will vary with depth depending on the rate of consolidation of the sediments. The change in porosity with time can thus be expressed

EQUATION (4)

Assuming an exponential function, as given by equation 1, and differentiating that function, we obtain

EQUATION (5)

LATERAL PORE PRESSURE IN SANDS

As indicated in the foregoing discussion, the sediments within the basin consist of alternating layers of sand and shale. For the purposes of analysis, the sand layers are considered to be laterally continuous. At some distance away, the sand layers are assumed to connect to the surface; either the sands crop out or some vertical conduit--perhaps a fault zone--acts as a path of higher permeability that allows for flow to the surface. The stratigraphy is portrayed diagrammatically in Figure 9. For the purposes of analysis we have taken a representative horizontal slice through the system. The geology of this slice is idealized as a wedge of sand with shale above and below as shown in Figure 10. Under such circumstances, the sand beds act as drains for both the underlying and overlying ompacting shale layers. Fluid from the compacting shales flows vertically into the overlying and underlying sands and then laterally in the sands to points of discharge.

Because of the geometry of the South Caspian basin, in our diagram the wedge of sand is terminated at one boundary. This termination represents a pinch-out of the sands toward the deep basin. Flow is pictured as approximately one dimensional in the sands, and in our particular study, from area III toward area I (south to north).

Fig. 6. Hydraulic head (within sand units) above land surface in areas I, II, and III.

Table 2. Shale Porosity vs. Depth for Areas I, II, and III

Fig. 7. Plot of shale porosity vs. depth for areas I, II and III; an exponential curve is fit to data for each area.

Fig. 8. Schematic diagram illustrating assumptions of: (1) a constant rate of basement subsidence, (2) a stable porosity vs. depth relationship with time, and (3) a sediment-water interface at zero.

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The deepest part of the South Caspian basin is situated south of our area III.

The system as depicted in Figure 9 is obviously a highly idealized schematic of the actual geologic system. We understand its limitations; this simplified picture, however, allows us to make what we believe is an enlightening analysis of the pore pressure.

For the purposes of analysis, we defined the geometry as depicted in Figure 10. The usual assumption made in the theory of consolidation (Terzaghi, 1925) is that the decrease in pore space represents an expulsion of fluid from the clays, and that all of this change in porosity represents a change in fluid content (i.e., the compressibility of the clay minerals is negligible). Under this assumption the rate of flow into a sand layer is given by

EQUATION (6)

where Q(x) = flow rate in the sand at point x (cumulative amount of fluid expelled from the overlying and underlying compacting shales is a function of x), z₁ = midplane of upper shale, z₂ = midplane of lower shale, S_shss/ = sand/shale ratio (a function of x), and x = distance from sand pinch-out.

Performing the integration we obtain

EQUATION (7)

Using equation 7, calculations to evaluate the flux coming from the shales were made for 1,000-m depth intervals for areas, I, II, and III; these results are plotted in Figure 11. The results suggest that the outflow from the shales at any given depth varies approximately linearly with distance toward the center of the basin.

If we assume that flow is essentially horizontal within one sand body (i.e., that vertical gradients in hydraulic head are negligible within the sand), we can write an equation for lateral flow:

EQUATION (8)

where b_ss(x) is the thickness of the sand layer, K is the hydraulic conductivity of the sand, h^prime is the excess hydraulic head (defined so that hydrostatic head is h^prime = 0), and S is the storage coefficient of the sand. Based on the sedimentation rate and sediment thickness the flow system within the sands at depths greater than 2,500 m has existed for times in excess of 2 m.y., we can assume

Fig. 9. Diagrammatic cross section of sand and shale in a basin similar to South Caspian basin.

Fig. 10. Cross section of idealized sand-shale sequence analyzed in this study.

Fig. 11. Rate of fluid outflow from shales into sands within South Caspian basin; curves are for 1-km depth slices from 0-1 km (top) to 4-5 km (bottom).

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steady flow (i.e., ^dgrvh^prime/^dgrvt = 0) and equation 8 becomes

EQUATION (9)

Integrating equation 9 once yields

EQUATION (10)

Equation 10 states that the lateral flow passing a point (x) in the sand must equal the cumulative outflow from the shales occurring over the distance 0 to x (from the sand pinch-out to point x). Figure 11 suggests that Q varies linearly across the basin. Thus we can state

EQUATION (11)

where ^agr and ß are constants. For the purposes of analysis, we further assume that the sand thickness also varies linearly across the basin and pinches out at x = 0. The thickness of sand at a given point (x) is

EQUATION (12)

For ease of later analysis, b_ss(x) may be expressed in terms of the derivative of the shale-sand ratio

EQUATION (13)

where m(x) = ^dgrvS(x)_shss//^dgrvx, and ^Dgrz = z₂ - z₁.

Substituting equations 11 and 13 into equation 10 yields

EQUATION (14)

Equation 14 is readily solved by separating the variables:

EQUATION (15)

We can evaluate the excess head at x = 0 (the sand pinch-out), by observing that the head is hydrostatic at x = L (the northern extremity of the sand wedge); that is, h^prime(L) = 0. Thus,

EQUATION (16)

Since h^prime(0) is the excess head at the sand pinch-out, it is the largest value of excess head within the sand wedge. Equation 16 can be rearranged so that the hydraulic conductivity of the sand may be expressed as a function of the excess head observed at x = 0:

EQUATION (17)

The results of evaluating equation 17 for depth intervals of 1,000 m are given in Table 3.

The calculated permeabilities are regional values; they represent an average value that applies to the zone of sand across its entire extent. The calculated permeabilities are substantially lower than the permeabilities that one would expect to encounter in a single sand body; the values represent the degree of interconnection of the sands. The amount of interconnection would be expected to be best in areas of high sand to shale ratio and poorest in areas of lower sand to shale ratio. The permeability values calculated in our simple model are indicative of an average amount of interconnection of the sands across the entire basin. One may reasonably expect that regional permeability across the entire basin would be one to two orders of magnitude smaller than the permeability of a singl sand body.

LOCAL FLOW: EFFECT OF VERTICAL CONDUITS

Vertical conduits for flow are thought to be important zones for the upward discharge of fluids in compacting sand-shale sequences. In the Gulf Coast of the United States, such vertical conduits are thought to be formed by

Table 3. Calculated Regional Sand Permeabilities

Fig. 12. Diagrammatic cross section of a compartmentalized flow system.

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faults that occur in the area. In the South Caspian basin, mud volcanoes are relatively common (Figure 5) and may also provide conduits for upward discharge.

If vertical conduits were high in hydraulic conductivity then one would expect the flow system to be areally compartmentalized and each compartment would have approximately the same hydraulic-head distribution (Figure 12). One would not expect to encounter a regional lateral gradient. Observe that a lateral horizontal gradient exists within the Caspian basin. The hydraulic head is higher in area III than in area II, and in area II the head is higher than in area I (see Figure 4). The fact that a lateral gradient exists across the basin indicates that vertical conduits are of sufficiently low hydraulic conductivity that they are not a significant outlet for the flow.

DISCUSSION

Several major assumptions have been made in our analysis, some of which may be worthy of additional comment. In simplifying equation 2 to equation 4, we assumed that the porosity vs. depth profile at any given location is stable with time. This assumption is equivalent to assuming that the rates of sedimentation and subsidence, as well as the ratio of sand and shale accumulation, are constant with respect to time. We believe this a reasonable assumption in a rapidly subsiding basin such as the South Caspian basin.

An additional implicit assumption exists in our analysis. We have neglected the water dispelled from the compaction of the sands themselves. We have assumed that the water derived from compaction of the sands is negligible compared to that which comes from compaction of the shales. This assumption is also, we feel, reasonable considering the difference in compressibility and thickness of shale vs. sand.

In addition to a lateral gradient in excess head, a vertical gradient occurs in excess head. This vertical gradient implies a component of upward vertical flow in the basin. Vertical flow is controlled by the hydraulic conductivity of shale, in contrast to horizontal flow, which is controlled by the hydraulic conductivity of sand. Because of the contrast in vertical to horizontal hydraulic conductivities, the rates of vertical flux are considerably less than the horizontal rates. We have formulated our analysis in such a way as to ignore the upward flow of fluids.

SUMMARY

1. The data for the South Caspian basin indicate that substantial differences in pore pressure exist between the sands and shales within the sedimentary sequence. This condition indicates that the sands are acting as drains for all fluids generated by the compacting shales.

2. A northward hydraulic gradient is present in excess head, indicated by the data, from the basin interior toward the basin margin. This gradient indicates regional groundwater flow within the sands. The results of our first-order mathematical analysis indicate that a regional sand permeability of 1-30 md would account for the excess hydraulic head (observed within the sands in areas II and III) as the result of regional groundwater flow.

3. If discharge from the basin also occurs through vertical conduits, these vertical conduits must be relatively impermeable in order to preserve the observed excess hydraulic head in the sands.

The results of this investigation have important ramifications regarding the migration and accumulation of oil and gas. The lateral flow within sand layers implies that the stratigraphic sequence is divided into horizontal units that are hydraulically well isolated from one another. This idea is not new, and is the basis of much of regional groundwater movement theory dating back to Chamberlin (1885) and Darton (1909) at the turn of the century in the United States. Chapman (1972, 1973) showed the importance of this hydraulic isolation to the accumulation of oil and gas.

Our focus in this investigation was on the South Caspian basin. However, we believe that the situation we observe in the South Caspian basin could also operate in other actively subsiding basins.