Exploration in deeper parts of sedimentary basins requires a better understanding of the rate and timing of quartz cementation, one of the main factors controlling reservoir quality in well-sorted sandstones.

In the recent literature on sandstone diagenesis, quartz cementation is frequently interpreted as having occurred at relatively shallow depths and at low temperatures. In continually subsiding sedimentary basins like the North Sea and the Gulf Coast, however, sandstones buried to less than about 2.5-3.0 km have very little quartz cement. Fluid inclusion data from North Sea reservoirs indicate that most of the quartz cement forms at temperatures exceeding 90-100°C. Fluid inclusion temperatures in quartz overgrowths commonly approach bottom-hole temperatures, suggesting that quartz cementation may continue, probably at a reduced rate, after oil emplacement. Evidence of local dissolution of quartz by pressure solution is usually well developed in North Sea sandstones that contain si nificant quartz cement, but the volume of silica released is difficult to quantify. Amorphous silica and opal CT may be important sources of silica for quartz cementation at 70-80°C, and the existence of such metastable silica phases at lower temperatures is evidence that quartz does not then precipitate for kinetic reasons. Modeling shows that diffusion of silica is insignificant on a large scale (hundreds of meters), but is important on a smaller scale, particularly when amorphous silica and opal CT are present. At higher temperatures, the pore water will approach equilibrium with respect to quartz. Quartz precipitation will then result from upward (cooling) pore water flow.

Calculations show that if enough silica to precipitate a significant volume of quartz (1%) from external sources is to be introduced into sandstones by pore water flow, a flux of about 10⁸ cm³/cm² would be required. Such fluxes could be obtained only on a local scale and by assuming an extreme degree of focusing of compactional water or by thermal convection.

Modeling of coupled carbonate and silicate reactions can be useful in constraining our theories of solid transport in sedimentary basins. Calculations indicate that for cooling (rising) pore water, the rate of calcite dissolution exceeds the rate of quartz cementation by a factor of 30 to 300, depending on the pH of the pore water, which is assumed to be buffered by the silicate minerals. If the pore water is buffered by the carbonate system, the rate of calcite dissolution upon cooling is smaller, but still several times higher than for quartz. If significant volumes of quartz cement are introduced by advective flow of cooling pore water, all calcite present should, in most cases, have been dissolved, given the higher reverse solubility/temperature function of carbonates.

We suggest that the source of quartz cement in sandstones is predominantly local (<10 m), sourced from within the sandstones, mainly by pressure solution. Therefore, one must predict the porosity loss in reservoirs from internal textural and mineralogical properties of the sandstones in addition to temperature and pressure.

INTRODUCTION

Quartz cement is responsible for much of the porosity and permeability reduction in well-sorted quartz-rich sandstones that have been buried deeper than 3 km. The percentage of quartz cement vary greatly in the Jurassic Brent Group of the North Sea at depths exceeding 4 km and is then the main factor controlling porosity, which may range from less than 10 to 20% (Bjorlykke et al., 1992; Giles et al. 1992; Harris, 1992). Predicting porosity trends, both on regional and on reservoir scales, recently has become more important as exploration in many basins focuses on deeper reservoirs. Therefore, one must understand the processes controlling quartz

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dissolution and precipitation. Identifying the sources of silica that contribute to quartz cementation during diagenesis is the main problem. However, quantifying the volume of dissolved quartz and other silicates petrographically also can be difficult. In cases where there is abundant quartz cement but little evidence of quartz dissolution, the source may be difficult to identify. The timing of quartz cementation relative to temperature and burial depth also is important in terms of predicting porosity loss as a function of progressive burial.

We present two end member models. (1) Most of the silica precipitated as quartz cement is derived from local sources and transported mostly by diffusion over distances of a few centimeters up to meters. (2) A large percent of the quartz cement is derived by pore-water flow from sources some distance (>10-100 m) away from the site of precipitation.

In the model 1, the rate of quartz cementation will strongly depend on the rate of dissolution of silicate minerals and amorphous silica within the sandstones and adjacent shales. In model 2, the distribution of quartz cement would be primarily a function of pore-water flow. If most of the silica is "imported" from sources several meters away from the sandstones, one must base predictions of the degree of quartz cementation (and porosity) on models for pore-water flow. Assuming that the pore water is in equilibrium with quartz, the rate of cementation is a direct function of the vertical component of the pore water flux and geothermal gradient. In this paper, we discuss these two alternative hypotheses for the source of SiO₂ by reviewing data on the distribution of quartz c ment in sandstones from sedimentary basins, mainly the North Sea Basin and the Gulf Coast, and by presenting theoretical models for transport of silica in pore water.

TEMPERATURE OF QUARTZ CEMENTATION IN SEDIMENTARY BASINS

The timing of quartz cementation relative to burial can be inferred from textural evidence, isotopic analyses, and fluid inclusions. Important information also can be obtained from the distribution of quartz cement with depth in continuously subsiding basins.

Several authors have concluded that quartz cementation occurred at intermediate burial depths of 1-2 km (e.g., Gluyas, 1985; Dutton and Land, 1988; McBride, 1989). The main phase of quartz cementation in the Lower Cretaceous Travis Peak Formation (Gulf of Mexico) occurred at a burial depth of 1-1.5 km, with quartz cement derived from circulating meteoric fluids, according to Dutton and Diggs (1990). Several studies in other basins also concluded that quartz cementation occurred relatively early and predated precipitation of kaolinite and illite (Almon and Davis, 1979; Odum et al., 1979; Schmidt and McDonald, 1979; Tillman and Almon, 1979). In older sandstones, now exposed on land, quartz commonly is inferred to have precipitated relatively early at shallow burial. Girard and Deynoux ( 991) interpreted the quartz cement in upper Proterozoic quartzites from west Africa to have precipitated at 0 to 50°C, based on isotopic evidence.

Stable isotope analyses of quartz cement also may indicate temperatures of quartz cementation. The separation of quartz cement from the grains, however, is difficult and the isotopic composition of the pore water at the time of precipitation is usually poorly constrained. Frequently, isotopic compositions range from 16 to 20^pmil (Dutton and Land, 1988; Potocki, 1989; Brint et al., 1991; Girard and Deyneoux, 1991), but the range of temperatures inferred varies greatly. In Gulf Coast sandstones, the range

Table 1. Temperatures for Quartz Precipitation Measured from Fluid Inclusions in Reservoir Sandstones

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observed is between 14-34^pmil (McBride, 1989).

Microthermometry is important in terms of constraining the temperature of quartz cementation, and recent studies suggest that, in the case of quartz cement, there is little natural deformation in the fluid inclusions that could lead to erroneous measurements (Robinson and Glyas, 1992). Published fluid inclusion data from the North Sea Basin and Haltenbanken (Table 1) suggest that quartz cementation starts at about 80-100°C, and that the upper temperature limit increases with the present-day burial depth.

In the North Sea Basin, we find that sandstones buried to 1.5-2.5 km are still poorly indurated unless carbonate cemented, and have very little quartz cement. The Middle Jurassic Brent Group, which is the main reservoir sandstone in the northern North Sea, is extensively cored at depths between 1.8 and 4.5 km. Very little quartz cement is found in the sandstones buried to less than 2.5 km, and quartz cement generally increases with a burial depth of between 3.0-4.5 km (Bjorlykke et al., 1992; Giles et al., 1992; Ramm, 1992). A similar pattern of quartz cementation is observed in reservoirs from the Haltenbanken area (offshore mid-Norway), (Bjorlykke et al., 1986; Ehrenberg, 1990).

In the Miocene sandstones of the Gulf Coast region, quartz cementation seems to start at about 3 km burial depth, whereas the Pliocene sandstones do not show significant quartz cement in depths shallower than 4 km (Harrison and Summa, 1991). Sharp et al. (1988) stated that in the Cenozoic section of the Gulf Coast, quartz cement is found only in rocks heated to greater than 100°C. The higher temperatures required for quartz cementation in the youngest (Pliocene) sediments suggest a kinetic (time-temperature) control on porosity loss and quartz cementation (Bloch et al., 1986, 1990; Harrison, 1989). Early quartz cementation seems to be rare in continuously subsiding basins like the Gulf Coast and the North Sea.

SOURCES OF SILICA AND KINETICS OF QUARTZ CEMENTATION

Quartz cements in sandstones may be derived from several internal sources: (1) more soluble silica phases, e.g., amorphous silica (biogenic and volcanic) and opal CT; (2) dissolution of quartz, primarily by pressure solution; and (3) mineral reactions involving the release of silica from silicate minerals.

The solubility of the most common phases of SiO₂ as a function of temperature is illustrated in Figure 1. The kinetics of quartz precipitation is very important at low temperatures. At temperatures below 70-80°C, the rate of quartz precipitation is very slow, and less stable SiO₂ phases (amorphous silica and opal CT) are metastable; hence, the pore water remains supersaturated with respect to quartz. At higher temperatures, the reaction rate of quartz precipitation increases and the pore water approaches equilibrium with quartz. The transformation of opal A and opal CT to quartz is a time-temperature function, and calculations by Mituzatani (1970) show that it takes 10 m.y. at 50°C to transform 90% of a cristobalite phase to quartz. The rock composition however, influences the silica phase transformations (Isaacs, 1982). In Cretaceous and Tertiary shales from the North Sea, opal A is found down to about 1000 m below the sea floor and cristobalite down to about 1500 m (60-70°C) (Gran, 1989). The persistence of these metastable phases down to this depth indicates that the rate of quartz precipitation is very low. Amorphous silica, when dissolved, leaves little direct trace, but quartz cement precipitated from amorphous silica or opal CT commonly has a microcrystalline chert-like texture, which is related to the high degree of supersaturation during precipitation. Based on textural evidence, one commonly can determine when amorphous silica is the main source of quartz cement.

Silica also may be released from diagenetic reactions

Fig. 1. Concentration of aqueous silica in equilibrium with various silicates (thermodynamic data from Helgeson et al., 1978), and a synthetic pore-water profile. The synthetic pore-water profile is based on observations of recent sediments, reports in the DSDP/ODP volumes, and analyses of oil field formation waters. In recent sediments, the pore-water concentration of silica commonly approaches saturation with respect to silica. At intermediate depths (100-1000 m) transformation of amorphous silica phases to opal-CT controls the concentration of silica. Formation waters from reservoirs with an in-situ temperature higher than about 60°C commonly are in equilibrium with quartz. The region of minimum silica concentration is found at temperatures between 40 and 60°C (1200-1800 below sea floor if, as assumed here, the temperature gradient is 30°C).

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involving silicate minerals, e.g., the dissolution of feldspars and precipitation of clay minerals will release excess silica, as the following reactions show.

EQUATION

Leaching of feldspar (reaction 1) requires pore-water flow to remove the released potassium and sodium in solution, which also would remove silica released from feldspar dissolution and would prevent a further build-up of silica in the pore waters. If silica were allowed to build up in the pore water, smectite would precipitate rather than kaolinite. Thus, we must assume that much of the released silica is removed by the meteoric pore-water flow.

Meteoric water is normally supersaturated with respect to quartz. Blatt (1979) assumed a silica content of 32.5 ppm in pore water in the shallow subsurface. The low temperatures at shallow depths, however, are likely to prevent quartz precipitation during meteoric water flushing. As discussed, many sandstones that have been subjected to extensive meteoric flushing and feldspar leaching, like the Brent Group in the North Sea, show little evidence of quartz cementation at shallow depths.

At higher temperatures, when all of the amorphous silica and opal CT is dissolved and the silica is precipitated as quartz, the silica concentration in the pore water would then be controlled by quartz saturation. The source of silica to form quartz cement must then be silicate minerals, such as feldspar and quartz, or certain clay reactions (reactions 2 and 3). K-feldspar becomes unstable in the presence of kaolinite at temperatures exceeding 130°C, releasing silica, which may precipitate as quartz cement (Bjorlykke, 1983). Transformation of smectite to illite also would consume potassium and release silica into the pore water (Boles and Franks, 1979). To what extent the released silica is precipitated as quartz in the shales or transported into sandstones is still not well know . Calculations of the pore-water flux required for mass transfer by advection suggest that there is not enough water available to introduce significant volumes of silica into sandstones from shales (Bjorlykke, 1979). If the silica concentration in the shales is higher than in the sandstones, diffusion could be significant over shorter distances (<10 m). In an alternating shale/sand sequence, the shales may contribute silica by clay reactions and pressure solution, but thicker shale sequences are not likely to contribute much to the silica content in sand-dominated sequences.

The solubility of clastic quartz is probably not much higher than that of authigenic quartz cement, unless the clastic quartz is fractured or dislocated. Quartz, therefore, will dissolve mostly where there are local conditions, such as pressure solution, that create an increase in the solubility of quartz. However, large crystals forming quartz overgrowths are more stable than fine-grained quartz, which has a higher specific surface area (Williams and Parks, 1985). Silt- or clay-size quartz in sandstones thus may dissolve totally and leave very little trace. Irregular clastic sand grains also will have a higher surface area than quartz grains with large quartz overgrowths; therefore, the grains with early quartz overgrowth may continue to scavenge much of the silica released into the ore water. Carbonate cement may cause dissolution of quartz due to an increased pH, and, if a solubility gradient is established, silica will

Fig. 2. A comparison of the direction and magnitude of the flux of dissolved silica caused by molecular diffusion ("Diffusion" curve) and the flux caused by sedimentation and sediment compaction ("Pore-water burial" curve). The calculations of the fluxes (Appendix) are based on the assumption of a constant rate of sedimentation (30 m/m.y.) and that the system is at steady state with respect to silica (Figure 1). The silica minimum causes diffusion of silica into the zone both from below and above. At about 1000 m, a local maximum in the concentration of silica (the gradient is zero) occurs, from which silica diffuses up toward the surface and down toward the minimum. Continuous sedimentation causes the advective flux with the sediment surface as reference to be downward (positive) at ll depths. The advective flux is given by the product of the rate of burial of pore water and the silica concentration. The advective term increases more rapidly below 2000 m than predicted by the pore-water profile alone because the rate of compaction decreases with increasing depth (the rate of pore-water burial increases). Note that, at all depths, the total flux (the sum of the diffusion and advection terms) is positive, i.e., downward.

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be transported by diffusion from the areas of dissolution to the sites of authigenic quartz crystals. Pressure solution is caused by a local increase in quartz solubility at grain contacts or along stylolites. Mass balancing the volume of dissolved quartz against the volume of quartz cement on the basis of textural evidence is very difficult. The volume of dissolved quartz at grain contacts, to a certain extent, can be estimated from textural studies, and cathodoluminescence helps one distinguish between clastic grains and cement (Houseknecht, 1989). A quantification of how much is dissolved at grain contacts depends on assumptions about the original grain shape and thus is rather subjective, but it is possible to obtain an estimate of how much has been dissolved. In the case of stylo ites, the relief of the stylolites can be taken as a minimum figure of how much is dissolved, but it is not possible to quantify the upper limit of quartz dissolution. Tada and Siever (1989) listed five different published methods of estimating the thickness of dissolved material and concluded that estimates of dissolved quartz commonly are ambiguous. In addition, thin clay laminae, which are not developed into stylolites, also may represent areas of quartz dissolution.

At the thin-section scale, one should not attempt to establish total mass balance between the amount of quartz dissolved and precipitated. Samples taken between stylolites and clay laminae may show only evidence of quartz overgrowth.

TRANSPORT OF SILICA IN PORE WATER

Transport of Silica by Diffusion

At higher temperatures (>70-80°C), when the reaction rates are higher, we may assume that the pore water is in equilibrium with quartz (Iijima, 1988; Hutcheon, 1989). Diffusion of silica would result from the concentration gradient in pore water, which is in equilibrium with quartz. Because the solubility of quartz increases with temperature, the diffusion will be mostly upward. Where amorphous silica is present, a decrease in silica concentration with depth may occur within a certain depth interval (^sim1.5 km) near the transition from amorphous silica and opal CT to quartz (Figure 1) and diffusion could also be downward (Figure 2). One may expect a convergence of silica by diffusion upward and downward in the depth interval of 1.5-2.0 km (Figure 3).

We calculated silica/depth profiles assuming equilibrium between the pore water and different silica phases. Assuming equilibrium with quartz at elevated temperatures (>70°C), and equilibrium with opal CT and amorphous silica at lower temperatures, we estimated a synthetic silica profile.

As a first approximation, one may estimate the reaction rates by taking the depth-derivative of the flux and assuming steady state (Appendix). The reaction rates calculated here (Figure 3) are the net rates, i.e., the difference between the rates of dissolution and precipitation within a given volume. We did not include local dissolution of silica phases and precipitation of more stable phases. This calculation shows a narrow zone of relatively high rates of silica precipitation at about 1600 m depth with net silica dissolution above and below this level. The peak in the dissolution rate above this level is due to the high concentration gradient in this region. Below this level, however, where the pore water is in equilibrium with quartz, although the diffusion is upward, each layer r ceives more silica from the underlying

Fig. 3. Net reaction rate estimated by taking the first derivative of the silica flux with respect to depth (Appendix). "Diffusion" is the first derivative of the diffusive flux (Figure 2), "Pore water burial" is the first derivative of the flux caused by sedimentation and sediment compaction (Figure 2), and "Total" is the sum of these two terms (the total net rate of reaction). The contribution to the net reaction rate by the diffusion term may be rationalized as follows. At a depth of approximately 1000 m, there is a local maximum in the concentration of silica from which silica diffuses both downward and upward, hence, the rate of dissolution must be high to supply the silica. To maintain the minimum silica concentration at about 1600 m, this region must be characterized by precipi ation. At greater depths, the contribution to the rate of reaction by the diffusion term approaches zero, but remains negative. This is caused by the fact that, although the direction of diffusion is upward, each layer receives more silica by diffusion from below than it contributes to the layer above. The contribution by the advective term may be rationalized as follows. Because we assume steady state, a given volume of water must lose silica as it is buried in the zone of minimum silica concentration (negative rate). Conversely, as the parcel of water is buried to greater depths, silica must dissolve (positive rates) to keep the water saturated with respect to quartz.

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sequence than it loses by upward diffusion.

The total volumes of quartz precipitated depend on the time each volume of sediments has resided at the different depth intervals. The total volume is found by integrating the ratio between the reaction rate and the burial rate. Figure 4 shows that after burial to 5 km, the total volume of quartz dissolution is 0.08 mole/m³ (using a sedimentation rate of 30 m/m.y.), less than 0.001% of the total rock volume. This calculation shows clearly that long-distance diffusion (>100 m) driven by solubility gradients is not significant in terms of supplying quartz cement from outside sources. Even when integrated over a period of 10⁶-10⁷ yr, this mechanism cannot account for a significant volume of quartz cement (Figure 4).

Transport of Silica by Pore Water Flow

If the silica concentration in the pore water is at quartz saturation, the rate of precipitation or dissolution of quartz due to pore-water flow can be calculated from the solubility/temperature function, which we call the thermal mass transfer coefficient, ^agrT (Wood, 1986). In the range of temperatures pertinent to diagenetic reactions (50-150°C), this coefficient is 1-3 ppm/°C.

The volume of quartz cement (Vq), which precipitates or dissolves due to advective flux (F) perpendicular to the isotherms, is then a function of ^agrT and the geothermal gradient (dT/dZ):

[EQUATION]

Where ß is the angle between the direction of flow and the isotherms and p is the density of the mineral (quartz). In the case of pore-water flow driven by compaction,

[EQUATION]

If the geothermal gradient (dT/dZ) is 30°C/km or 3 × 10^-4°C/cm, ^agrT = 10^-6 and ® = 2.7 g/cm³, then Vq = F × 10^-10. From this it follows that F = 10¹⁰ × Vq and, consequently, precipitation by advective flow of quartz cement corresponding to 1% of the rock volume requires a flux of 10⁸ cm³/cm². This is a very high flux, which can only be generated under very special conditions. At 3 km burial depth, the underlying sediments down to 6-7 km may have an average porosity of 10-20%. The total volume of pore water that potentially can be expelled vertically from the underlying sediments by compaction is then, in the case of complete dewatering, approximately 5 × 10^{4 /SUP> cm3/cm2. Compactional flow therefore must be focused by a factor of about 104 to cause significant cementation. This calculation assumes a complete dewatering of the underlying sequence, which is normally not the case. In a sedimentary basin with a constant rate of subsidence and sedimentation, the upward flow of pore water due to compaction is lower than the rate of subsidence (Bjorlykke et al., 1989; Caritat, 1989). Thus, as an average for the whole basin, there is no net upward pore-water flow relative to the sea floor. If the geothermal gradients remain constant, compactional water will not be subjected to cooling and therefore will not precipitate quartz. Only locally will pore-water driven by compaction be focused and have an upward flow rate hat exceeds the rate of subsidence. These calculations show that the degree of focusing of compactional water must be very high. Focused pore-water flow cannot explain diagenetic features ubiquitous in reservoir rocks, because focused pore-water flow can cause cementation only very locally and in small volumes. Additionally, focused pore-water flow would not likely preferentially flow through hydrocarbon traps, particularly in the case of tilted sandstone beds truncated by an unconformity, which are so common in the North Sea Basin.}

If silica precipitating as quartz cement is introduced from outside a sandstone by fluid flow, as suggested by Gluyas and Coleman (1992), the volume of quartz cement precipitated would be expected to be

Fig. 4. The cumulative amount of SiO₂ dissolved in each volume of sediment during burial from the surface to 5 km depth in response to a fixed sedimentation rate of 30 m/m.y. (Appendix). Figure 3 shows that the net rate of reaction is positive (dissolution) from the surface down to about 1500 m. The result is that, when buried to this depth, each cubic meter of sediment has lost about 0.08 mole of silica. The high rate of precipitation of silica in the zone of the silica minimum rapidly compensates for the amount lost above. From about 2300 m downward, the net rate of reaction is positive (dissolution), and when buried to 5000 m, each cubic meter of sediment has lost about 0.08 mole of silica. This corresponds to less than 0.001% of the volume of solids.

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proportional to the pore-water flux. The most permeable parts of sandstones would then receive most of the quartz cement and gradually become less permeable. A homogenization of the permeability would result from advective transport of silica. Typically, however, the permeabilities observed in sandstones vary greatly.

Pore-water flow by convection has been put forward by several authors as a mechanism to move solids in solution in the subsurface (Cassan et al., 1981; Wood and Hewett, 1982, 1984; Haszeldine et al., 1984b; Davis et al., 1985). Mathematical modeling of Rayleigh convection have shown that relatively thin shales (0.1 m) or cemented intervals within a sandstone sequence will effectively divide potentially large convection cells into smaller ones, which may then be too small to exceed the critical Rayleigh number (Bjorlykke et al., 1988). If the critical Rayleigh number is exceeded by as little as 10%, however, pore-water flow due to Rayleigh convection is fast enough to dissolve and precipitate 10% of the quartz within 10 m.y. (Palm, 1990). Thus, if Rayleigh convection is taking place, t e effects on diagenesis would be fast enough to be observed. Where the isotherms are not horizontal, there will always be some non-Rayleigh convection, but the velocities will be low and very significant in terms of transporting silica unless the isotherms are relatively steep (Bjorlykke et al., 1988).

The forces driving thermal convection are rather weak and the pressure gradient must be close to hydrostatic. If not, the pore-water flow will be unidirectional from areas of higher to lower potential, typical of compaction-driven flow.

Coupled Precipitation/Dissolution of Carbonate and Quartz During Convective Pore Water Flow

Even if convective flow should be relatively insignificant under most conditions in sedimentary basins, we believe it important to model the effect of such flow and also the effects of other types of advective flow.

Advective pore water will cause dissolution or precipitation not only of quartz, but also of other minerals that have temperature-dependent solubilities. In sandstones, we have very complex solubility functions for many of the common minerals. The solubility of calcite depends on the pH and pCO₂, and normally shows a solubility gradient reverse that of quartz. In a convection cell, the pore water can be assumed to be relatively homogeneous, and the concentrations of the dissolved components are essentially functions of changes in temperature and pressure within the cell. We calculated the ratio between quartz precipitation and calcite dissolution at different pH and depth (temperature) (Figure 5). The exact ratio between the volume of calcite dissolved and the volume of qua tz precipitated depends on the mechanism controlling pH. The pH of formation water is probably buffered by the silicate minerals (Hutcheon, 1989; Hutcheon and Abercrombie, 1990; Smith and Ehrenberg, 1989).

A pH between 4.5 and 6.0 is most probable for pore water in sedimentary basins. Seventy-three different samples of formation water from North Sea reservoirs had measured pH values between 6 and 7 (Egeberg and Aagaard, 1989). Recalculating the pH compensating for degassing of CO₂, the pH falls to between 4.4 and 6.1, with an average of 5.4 (Egeberg and Aagaard, 1992, personal communication). At about 3 km depth, the ratio between the volume of calcite dissolved and quartz precipitated on the upward-flowing limb of the cell will be 20 at pH 6 and 100 at pH 5. Even if 10% of the carbonate

Fig. 5. The solubility of quartz increases with increasing temperature, whereas calcite is the opposite. Thus, in a convection cell with higher temperature in the bottom than at the top, silica will dissolve at the bottom and precipitate at the top. Calcite will dissolve at the top and precipitate at the bottom. This figure shows the ratio between the volume of calcite and quartz precipitation in a 200-m high convection cell for a thermal gradient of 30°C/km. No precipitation or dissolution takes place in the vertical limbs of the convection cell, and the pH is controlled (and kept constant) by the silicate system. Because the temperature dependence of the solubilities of calcite and quartz differ most at low temperatures, the ratio between the volume of quartz precipitated and t e volume of calcite dissolved is higher at shallower depth (lower mean temperature in the convection cell). The calculations were done in the manner of Wood (1986) (mass balance on carbon and charge balance). The nonlinear system of equations was solved numerically. Because our system is considerably more acidic, we do not observe the retrograde behavior that Wood observed with an initial pH of 10.5 (Wood, 1986).

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cement or fossils is dissolved, only very small quantities of quartz (0.5-0.1%) could be precipitated at 3 km depth. At lower temperatures (2 km depth), these ratios will be even higher (ranging from 50:1 to 350:1). Thus, if trace amounts of calcite cement or fossils have not been dissolved, very little quartz cement can be introduced by convective flow. On the downward-flowing limb of the convection cell, where the pore water is being heated, massive calcite precipitation would be expected to occur if quartz of any significance is being leached. We conclude that if reservoir sandstones contain calcite cement or calcareous fossils, carbonate cement would block the downward pathway before much silica is moved.

The calculations made for convective flow cannot be applied directly to compaction-driven flow, because pressure gradients can cause rapid reductions in pCO₂. However, except where steep pressure gradients with rapid release of CO₂ occur, upward-moving (cooling) pore water would tend to dissolve carbonate and precipitate quartz. The presence of small amounts of calcite cement, common in many reservoir rocks, restricts the amount of quartz precipitated except under very local and special conditions.

If the pH of the pore water is not fixed, but is controlled by the carbonate system, the ratios between dissolved calcite and precipitated quartz are smaller (Figure 5), but the amount of calcite dissolved would still be several times larger than the volume of quartz precipitated if the pore water is in equilibrium with both minerals.

When modeling advective transport of silica, one must consider the effect on other minerals. Carbonate minerals, which normally have a retrograde solubility with respect to temperature, may help constrain the amount of silica transport. The presence of calcite cement in reservoir rocks limits the advective supply of silica, except under local conditions of rapid pressure reduction and CO₂ degassing.

CONCLUSIONS

Sandstones in continuously subsiding basins, such as in the North Sea and the Gulf Coast, tend to have poorly developed quartz cement down to a depth of 2.5-3.0 km. This observation contrasts sharply with the many interpretations of early quartz cementation at relatively shallow burial depths and lower temperatures in other sandstones.

Amorphous silica and opal CT may be important internal sources of quartz cement at burial depths of 1.5-2.0 km (70-80°C). At greater depth, both pressure solution and reactions between silicate minerals are the main sources of silica for precipitation of quartz cement.

Although silica is released as a result of feldspar leaching during meteoric water flushing, very little quartz is likely to precipitate during the flushing due to low temperatures and continued removal of the released silica.

Fluid inclusion studies from the North Sea Basin indicate that quartz cementation starts at about 90-100°C and continues during further subsidence, up to maximum burial or until most of the porosity is lost. Fluid inclusion data also suggest that quartz cementation may continue after oil emplacement, although the rate of quartz precipitation may be retarded.

Import of silica by advective transport from sources outside the reservoir sandstones would require very large pore-water fluxes (>10⁸ cm³/cm²) to supply significant volumes of silica. Advective transport of silica would imply that the highest precipitation rates would occur in the most permeable beds, thus blocking the most permeable pathways.

Diffusion of silica in pore water is insignificant as a mechanism for long-distance (>10-100 m) transport of silica.

Thermal convection probably is not important except around hydrothermal intrusions and salt domes. Calculations show that during thermal convection, cooling pore water would remove carbonate many times faster than quartz can be precipitated.

Pore-water flow driven by compaction also will normally dissolve carbonate at a much faster rate than quartz will precipitate. The presence of widely distributed carbonate cement or calcareous fossils, even in small amounts, suggests that significant amounts of silica cement were not introduced from an outside source by advection.

Prediction of quartz cementation and porosity loss in sandstone reservoirs must be based on the burial history, temperature and pressure, and also on the local sandstone petrography, which may help determine rates of dissolution and precipitation of quartz.

APPENDIX

Calculation of the flux of dissolved silica relative to the moving sediment surface requires a diffusive and an advective term

[EQUATION]

where D(X) = diffusion coefficient, C(X) = the concentration of silica, P(X) = the porosity and V(X) is the pore water flow rate relative to the sediment surface.

P(X) was taken as

[EQUATION]

where, P⁰ is the porosity at time of deposition and P^{^infinity} is the fully compacted porosity.

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D(X) is expressed as a function of the porosity and the pore water viscosity (µ)

[EQUATION]

where D⁰ is the diffusion coefficient of silica in free water and µ(X) is the temperature-dependent viscosity of the pore water. The rate of burial of pore water relative to the sediment surface V(X) may be expressed as

[EQUATION]

where S is the rate of sedimentation. This expression is valid for basins after the deepest sediments are fully compacted (P^{^infinity}). Figure 2 shows that diffusive and advective transport of silica along the synthetic concentration gradient depicted in Figure 1 are of similar magnitude. However, whereas the compactive flux is always downward, diffusion transport of silica is according to the local concentration gradient. The mass balance of dissolved silica within a volume of thickness ^dgrvX may be expressed as

[EQUATION]

where R(X) is the net rate of dissolution of silica phases. By assuming steady-state porosity and concentration profiles R(X) is given by

[EQUATION]

Figure 3 shows that as pore water is buried in the transition zone between high silica concentrations above and quartz saturation below, there is a peak in the rate of silica precipitation from the flow term (pore water burial). Also, because of the concentration gradients in this region, silica diffuses in, hence there is a negative contribution to R(X) by the diffusion term. To supply this silica, there must be relatively intense dissolution immediately above this zone; hence, the positive contribution from the diffusion term immediately above this zone. Below about 2500 m, there is net dissolution of quartz. However, this is caused by the burial term, and not by the diffusive term. Due to the concentration gradient, there is an upward diffusive flux of silica. However, because of t e shape of the concentration profile (the second derivative is positive below 1500 m) each layer receives more silica by diffusion from the layer below than it loses by diffusion to the layer above. Hence, the negative contribution by the diffusion term. Because pore water moves downward relative to the sediment surface, it is heated and dissolves silica. Pore water moves downward, gets heated, and dissolves quartz. Thus, the widespread contention that compactive flow of pore water may be a source of silica cement is a fiction. Adding the diffusive term and the flow term obtains the total rate of dissolution of silica. Nowhere is this rate greater than ±0.006 mole/m²/m.

What is the importance of this transport of silica in terms of volumes of solid phases dissolved and quartz cement precipitation?. The answer to this question can be found by integrating the ratio (rate of reaction)/(rate of burial):

[EQUATION]

where R(Z) is the net reaction rate at depth Z, and W(Z) is the burial rate of the layer at depth Z. The burial rate of sediment relative to the sediment surface W(X) may be expressed as

[EQUATION]

The inverse relation with the rate of burial is intuitively obvious. If a sediment layer spends a long time (low rate of burial) in the quartz precipitation zone, it will receive more cement. Figure 4 shows that silica dissolves all the way from the surface to a depth of approximately 1500 m. As sediments are buried in the transition zone they gain silica, and at about 2000 m this gain has balanced the loss from the layer above. At a depth of approximately 3500 m the amount gained in the precipitation zone has also been balanced. Below this depth the rate of loss of silica is approximately constant.

However, the most interesting feature is the scale of changes that take place. At no stage of burial is the net gain or loss of silica more than 0.08 mole/m³. This corresponds to less than 0.001% of the volume of solids.