INTRODUCTION

The world's deepest petroleum exploration well was drilled to a depth of 31,441 ft (9583 m) in the Anadarko basin of Oklahoma. However, deep basins, like the Anadarko, can have as much as 50,000 ft (15,240 m) of sediments, and the deepest parts of these basins represent a major frontier area for gas exploration. It is important to understand the factors that control gas composition and survival in this deep environment and to be able to predict deep gas composition. Even some basins that are currently relatively shallow have been buried much deeper in the past, and their gas content and composition has probably been controlled by the past deep burial.

Crude oil and natural gas (together called petroleum in this paper) are generated from the organic matter incorporated into sediments as they are deposited. On burial, rising temperature and passing time drive the petroleum generation process, and the conversion of organic matter to petroleum is kinetically controlled. The process is independent of the nature of the rock matrix, and generation appears to proceed in essentially the same way in both clastics and carbonates. As temperature continues to rise, the rate at which the organic system moves toward equilibrium steadily increases. In an inert system, the stable end products will be methane and graphite (although true crystallographic graphite will not be formed until rock metamorphism occurs). When gas composition is controlled t ermodynamically, all of the minerals in the system may be involved, so rock mineralogy can have a critical role in determining gas composition.

Kinetically controlled reactions that generate oil and gas are time dependent; in contrast, the composition of systems that are in thermodynamic equilibrium are independent of time (Figure 1). Thus, the ages of oils, gases, source rocks, and reservoirs do not appear in thermodynamic calculations, and the results are independent of geologic age. At shallow depths, equilibrium will not be reached and thermodynamically unstable materials (such as crude oil) can be found. At present, the depth where gas composition is controlled thermodynamically is not

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known, but the approach to equilibrium is favored by high temperatures and long time intervals, and a thermodynamic approach to calculating deep gas composition is likely to be valid only for depths greater than approximately 25,000 ft (7620 m) for an average geothermal gradient.

Gas that has migrated up from depths greater than about 25,000 ft (7620 m), but is currently in shallow reservoirs, will have a gas composition controlled by the mineral assemblage present during deep burial. At depths greater than X in Figure 1, the gas composition is controlled thermodynamically and so depends on temperature, pressure, and rock composition. On uplift, the rate at which reequilibration is achieved will steadily diminish, until at some point the kinetics become so unfavorable that the reaction essentially stops and the gas composition is "frozen in." During uplift from depth Y to depth X (Figure 1), gas composition continues to adjust rapidly and remains in thermodynamic equilibrium at each transient set of ambient conditions. Thus, for a given bulk composition, the a tual composition at depth X will be the same regardless of the depth represented by Y. This suggests that the gas composition in shallow reservoirs that were once deeply buried is not controlled by the greatest depth of burial, but rather by the shallowest depth at which the gas composition was in thermodynamic equilibrium with the local mineral assemblage.

In a previous paper (Takach et al., 1987), we discussed some aspects of the survival of natural gas in deep reservoirs and outlined a thermodynamic approach to the problem of predicting gas composition in the deep subsurface. Only simple illustrative examples were presented, and they were selected mainly to demonstrate the computer procedures that had been developed. In this paper, we consider deep clastic systems that are more significant to the geologist exploring for ultradeep gas.

THERMODYNAMIC CALCULATION OF GAS COMPOSITION

Equilibrium compositions were calculated using a modified version of a computer program described by Dayhoff et al. (undated). In an earlier paper (Takach et al., 1987), we presented a detailed description of how the program works, a block diagram, a listing of the thermodynamic data used, an input file for a hypothetical complex mineralogy, and several tables showing the type of output generated at each depth of interest. Since the earlier paper, only minor modifications involving the presentation of output have been made.

The program can handle up to 25 elements distributed among a maximum of 70 compounds in up to 20 phases. When a calculation is performed, the

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program automatically retrieves each compound's elemental composition and free energy as a function of temperature from a database. Rough initial guesses of concentrations of the compounds for each mineralogy are used to define the elemental composition for the system. Each system's composition consists of two types of compounds: "majors" and "traces." Major compounds are those that are considered to be quantitatively most important in each mineralogical system. For example, each sandstone mineral assemblage investigated in this paper contains quartz as the dominant mineral, ranging from 72 to 90% by volume of the system, and a varying number of other minerals, each of which comprise 2% by volume. Minor compounds are offered to the program at the minimum allowable concentration, which is a mole fraction of 0.00001. This provides a way of entering mineral phases that may not be present in the rock initially but may be formed by reaction if a major compound containing a similar composition is less stable and its concentration diminishes. For each mineral assemblage used, the pore space was assumed to remain constant at 10% of the rock volume, with 60% of this occupied by water and the rest by hydrocarbons. The chemical composition of the pore space with and without graphite, as well as all the mineral assemblages studied, are provided in Table 1 and the sections that follow.

Once defined, the elemental composition remains fixed throughout the computation, and the program calculates improved approximations of the compound concentrations. This is accomplished by adjusting the amounts of the compounds using an iterative procedure until a set is obtained that yields the minimum free energy for the system consistent with overall chemical composition, temperature,

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and pressure. The algorithm used in the program finds the local minimum closest to the input concentrations guessed. The calculation for a given system is complete ("system has converged") when in two successive iterations two conditions are met ("convergence criteria"). The first criterion is |DeltaX[i]{a}|/X[i]{a} < user specified value, where X[i]{a} = number of moles of the ith compound in phase a. The second criterion is |DeltaP[j]|/P[j] < user specified value, where P[j] is the partial molal free energy of the jth element. The potential problem of multiple minimum solutions can be probed by changing the relative amounts and compositions of the compounds while maintaining a constant overall elemental composition. For example, using 5C + 6CH[4] leads to the same calculated v lues as C[11]H[24]. A detailed description of the energy minimization method is in Dayhoff et al. (undated).

An important option available to the user of the equilibrium program is the ability to treat the major gases of a given system as though they are ideal or to treat them as real gases by calculating fugacity corrections. In many previous studies, ideal behavior has been assumed for all gases. Fugacity data for H[2]O, CH[4], CO, CO[2], H[2], C[2]H[6], and H[2]S were obtained from Burnham et al. (1969) and Ryzhenko and Volkov (1971). The data for fugacities as a function of temperature and pressure were curve fit using a polynomial-surface fit program and, for each gas, the order of the polynomial that gave the minimum error was chosen to represent the fugacity coefficient. The coefficients in the polynomial are stored and accessed by the program to calculate each gas fugacity at each te perature and pressure. This procedure gives a more realistic value for the free energy corrections for particular gases at high pressures and low to intermediate temperatures (as defined by the range of values in this study). The errors associated with the fugacity calculations are generally less than 10%, although they may be considerably more for water at high pressure and low temperature (primarily because, in this region, tabulated values contain only one digit). Even with these uncertainties, the results still approximate the real situation more closely than when ideal gas behavior is assumed.

No pressure corrections were made for the free energy of formation of solids. This correction would be minor, amounting to less than 1 kcal/mole at the highest pressures. Similarly, no pressure correction was applied for liquid water. Here again, errors of up to 1 kcal/mole can be expected. An error of this magnitude will affect the liquid-vapor distribution for water, but have only minor effects on other equilibria. Each volatile was offered to the program as either a pure gas (phase "G") or dissolved in the aqueous phase (phase "L"). When selected input files were tested with all the volatiles (except water) offered only as gases, the results for all the studied mineral assemblages showed that gases other than water vapor did not survive in mathematically significant quantities at a y depth. Gases suffered the same fate when the program was offered volatiles in both the aqueous and the gas phases. The equation for computing compound free energies does not favor free gases under the high pressures encountered in the deep subsurface. In considering the aqueous phase of a substance, the program retrieves free energies stored in the database for the gaseous form, but does not apply fugacity coefficients. Also, no corrections were made for heats of solution or heats of mixing, but these are not expected to have significant effects on the relative composition of dissolved gases. Finally, no ionic species have been included in the aqueous phase. Although this is not geologically realistic, only minor changes in the dissolved gas equilibria are anticipated.

CLASTIC RESERVOIRS

Any rock where adequate permeability and porosity are coupled with a seal can serve as a reservoir for oil and gas. Although there is production from igneous and metamorphic reservoirs, the vast majority of reservoirs are sedimentary rocks. Quartz sands and carbonates form the economically important reservoirs, and each of these two rock types contains roughly equal amounts of the world's petroleum reserves (Moody, 1975). In our paper, attention is focused on deep reservoirs that are dominantly siliceous.

The mineralogy of sandstone reservoirs varies widely, and an examination of methane stability in ultradeep sandstone systems must include the effects of clays, feldspars, carbonates, iron oxides, sulfides, and other minerals that may be present as detrital or authigenic phases and as intergranular cements. For convenience in this paper, we describe reservoirs in a sequence of increasing complexity of mineralogy starting with clean sands and sequentially adding various detrital and authigenic minerals. This is intended to illustrate program capabilities, but any appropriate temperature, pressure, porosity, and mineralogy could be investigated thermodynamically.

Output provided by the thermodynamics program includes the amounts of all of the minerals, gases, and liquids calculated for each given pair of temperatures and pressures. In ultradeep exploration, the main concern is with the composition of the gas that could be produced, and so we have chosen to present gas composition data on a water-free basis as a function of depth (see, for example, Figure 2). We selected 40,000 ft (12,192 m) for the maximum depth because that represents a reasonable extrapolation of current drilling technology and

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because thermodynamic data are reliable at the corresponding temperatures and pressures. The shallower part of the depth range shown in the figures is of theoretical interest only because, at these relatively low temperatures, reaction kinetics are more sluggish and the system will not be at thermodynamic equilibrium. There, actual compositions cannot be calculated by a purely thermodynamic method.

CLEAN SANDS

Average sands contain about 65% quartz, but those that have undergone considerable reworking or multiple cycles of transport and deposition have lost minerals that are either mechanically weaker or chemically less stable, and rock mineralogy is dominated by quartz.

In our study, clean sands were modeled by a system made up of 90 vol. % silica and 10 vol. % porosity. Gas saturation was assumed to be 40%, so the pore space contains 40% methane and 60% water. With significant increases in subsurface depth, porosity generally decreases to low values. The computer program can handle such changes but, for simplicity, we kept porosity constant at 10% for all the examples in this paper. Minerals that are not part of the original system but are possible reaction products are loaded into the program as trace compounds. For the "clean sandstone" system these included H[2]O vapor, CO[2], H[2], C[2]H[6], CO, and graphite, together with C[20]H[42] to represent crude oil (Table 1).

In some deep reservoirs, the gas was formed by the thermal cracking of crude oil and the methane will be accompanied by a graphitic residue (Takach et al., 1987). We have modeled this system by assuming that the reservoir pore space originally contained 40 vol. % oil and that this was subsequently cracked to graphite and methane. A mass balance approach to the thermal cracking of oil gives final products of 85 vol. % gas and 15 vol. % graphite (Barker, 1990), which leads to a final rock composition of 90% silica, 6% water, 3.4% methane, and 0.6% graphite (Table 1). This system is called "clean sandstone + C." Note that in these clean sandstone systems (and in all other systems considered in this paper), silica is treated thermodynamically as if it were quartz.

Equilibrium gas compositions for the "clean sandstone + C" system are shown in Figure 2. The horizontal scale is a cumulative volume percent so that, for example, at 20,000 ft (6,096 m) in Figure 2, the gas composition is 51.1% methane, 2.3% hydrogen, and 46.7% carbon dioxide. This figure also shows a steady decrease in the methane percentage with depth and a relatively minor decrease in the percentage of carbon dioxide. Hydrogen percentage increases with depth (the significance of this is discussed below). The absolute amount of methane in the graphite-bearing system decreases 56% from 0.0079 to 0.0035 moles over the depth range considered, but the concentration change is much larger (from 50.5 to 5.5%) because the addition of other gases, notably hydrogen, dilutes the methane. The f gures showing cumulative volume percent as a function of depth (e.g., Figure 2) give no information about the total volume of gas although this information is available from the program.

In the "clean sandstone" system without graphite, methane appears to go to zero at about 35,000 ft (10,668 m), but there are some additional complications because of the way trace components are handled. The minimum value that can be assigned to any individual compound is 0.00001 moles, and when there are a large number of traces (e.g., CO[2], CO, C[2], C[3], C[20]) the amount of carbon introduced becomes significant and distorts the amount of methane. An effective procedure is to run the program with all reasonable trace compounds to establish which ones always become zero. These are then removed and the program rerun to give final composition.

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When C[20] alkane and other hydrocarbons, such as benzene, are offered as possible compounds, the thermodynamic calculations show that they are never stable. Thus, crude oil is not stable at any subsurface depth and is found in nature only because it is kinetically stable and is moving toward the thermodynamically stable products at a rate which is slow, even on a geological time scale. This again serves to emphasize the fact that a thermodynamic approach to calculating subsurface hydrocarbon compositions is only valid for systems that are in thermodynamic equilibrium and cannot be applied at shallow depths. It is also consistent with the observed depth trend from oil to gas in deep basins.

Most calculations assume a normal (i.e., hydrostatic) pressure gradient of 0.47 psi/ft (Table 2), but abnormal subsurface pressures become increasingly common at greater depths and may approach the rock load of 1.0 psi/ft. Using a lithostatic pressure gradient of 1.0 psi/ft with the "clean sandstone + C" system leads to an equilibrium gas composition that differs very little from the one obtained for hydrostatic conditions, suggesting that the effect of pressure on gas composition is trivial. This is generally true, and gas compositions calculated at high pressures for the mineral assemblages discussed below are very similar to those calculated using hydrostatic pressures.

Geothermal gradients vary significantly. For the purposes of this paper, we used an average gradient of 25 degrees C/km. At a higher gradient of 40 degrees C/km, methane is less stable in the "clean sandstone + C" system and is eliminated by 30,000 ft (9144 m).

SANDSTONES WITH FELDSPAR
AND IRON OXIDES

As a second step in modeling sandstone reservoirs, we included 2 vol. % each of potassium feldspar (loaded as microcline), clay products (loaded as kaolinite, but also with muscovite mica), magnetite, and hematite (Table 1). Trace components included siderite as well as the usual array of higher hydrocarbons, and this assemblage was run both with and without graphite. The pore volume and its contents remained unchanged from the previous calculations.

In the absence of graphite, the methane content of the gas phase decreases from 50% to almost zero by 35,000 ft (10,668 m), whereas hydrogen content builds up. In contrast, the graphite-bearing system, shown in Figure 3, still has 6% methane at 40,000 ft (12,192 m). As expected, ethane and higher hydrocarbons are not stable in either system. In the graphite-bearing system, the graphite that is initially present is eliminated by reaction below 15,000 ft (4572 m). Mineralogic changes are relatively minor, with magnetite increasing at the expense of hematite down to 40,000 ft (12,192 m). Siderite, however, is not stable at any depth, and the potassium feldspar also decreases to quite low levels.

SANDSTONES WITH FELDSPAR
AND CALCITE CEMENT

The role of the carbonate cements was studied by adding 2 vol. % calcite to the reservoir mineralogy. If no other calcium-bearing phases are present, there will be no possible reactions involving the calcite and it will appear to be stable. Because of this, it is necessary to offer the program a range of possible calcium-containing phases, and we included anorthite, wollastonite, and laumontite. The equivalent graphite-bearing assemblages were also run. The gas composition without graphite is shown in Figure 4; the gas composition with graphite is shown in Figure 5.

In the absence of graphite, methane in the gas phase sharply decreases from 53% at 10,000 ft (3048 m) to 0.3% at 20,000 ft (6,096 m). Carbon dioxide rises from 9% at 10,000 ft (3048 m) to 99% at 40,000 ft (12,192 m) and is produced by the thermal breakup of the calcite, which steadily decreases in amount below 15,000 ft (4572 m) and is eliminated by 30,000 ft (9144 m) (see discussion following). In addition, methane may be oxidized to carbon dioxide.

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Methane percentages are considerably higher when the system contains graphite. At 10,000 ft (3048 m), equilibrium methane percentage is close to 100. It decreases steadily with depth to 5.3% at 40,000 ft (12,192 m). The decrease is due to increases in both carbon dioxide and hydrogen, which rise to 43.3 and 51.4%, respectively, at 40,000 ft (12,192 m). As in the nongraphite system, calcite is not stable at great depths.

SANDSTONES WITH FELDSPAR,
IRON OXIDES, AND CALCITE

The combined effects of the presence of both iron oxides and calcite cements were investigated in the next sandstone system considered. Figure 6 shows the results for the graphite-free system; Figure 7 shows the results for the graphite-bearing system. The trends of gas composition with depth are generally similar to those calculated for the "silica/feldspar/calcite" systems. In the absence of graphite, carbon dioxide increases with depth (corresponding to a decrease in calcite), and methane does not survive at any depth (Figure 6). In contrast, Figure 7 shows that in the graphite-containing system, methane percentages are considerably higher than those in the system without graphite. As observed for the systems containing calcite but not iron oxides, methane decreases with depth as c rbon dioxide and hydrogen concentrations rise.

SANDSTONES WITH FELDSPAR,
IRON OXIDES, CALCITE, AND SULFIDES

The final sandstone mineral assemblage considered included 2 vol. % pyrite and 2 vol. % anhydrite, with elemental sulfur and hydrogen sulfide offered at trace levels. In the absence of graphite, methane is not stable at any depth, and the gas phase is made up of carbon dioxide, hydrogen, and hydrogen sulfide (Figure 8). Hydrogen sulfide content increases slowly with increasing depth and reaches 19.2% at 40,000 ft (12,192 m). When graphite is added to the mineral suite, methane is present over most of the depth range and is quantitatively the most important gas down to about 22,500 ft (6858 m) (Figure 9). At greater depths, carbon dioxide and hydrogen dominate with hydrogen sulfide accounting for up to 15% of the gas phase.

Figures 8 and 9 (like Figures 2-7) show gas composition as a function of depth because composition of produced gas is of major economic importance. It is possible, however, that a component of the gas mixture may be quite thermodynamically stable but

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that its percentage contribution to the gas composition decreases because it is being diluted as quantities of other components increase. In addition to providing percentage gas compositions, the thermodynamic program also provides information on the number of moles of each component in the system, so it is possible to decide whether a particular component is being removed by reaction or simply diluted. In Figure 10, the moles of gaseous components are shown as a function of depth for the sandstone system with feldspar, iron oxides, calcite, graphite and sulfides. This shows clearly that methane is quite stable down to about 30,000 ft (9144 m). The figure also shows the buildup with depth of the absolute amounts (moles) of carbon dioxide, hydrogen, and to a lesser extent, hydrogen sul ide. As a consequence of these increases, the percentage of methane decreases rapidly with depth (as shown previously in Figure 9).

HYDROGEN

The thermodynamic calculations show that in the deeper, hotter parts of most of the systems examined hydrogen becomes a major component. Although natural gases with significant hydrogen have been reported in many areas of the world, they are not common (Goebel et al., 1984; see also Coveney et al., 1987, and references cited by them). Unfortunately, the database is poor because hydrogen content is often not analyzed, and in addition, the containers commonly used for sampling natural gas rapidly loose hydrogen. The presence of hydrogen in natural gas implies that something in the system has been oxidized, and the conversion of ferrous to ferric iron is usually suggested. For example, high hydrogen gases occur in Oman in association with serpentinized ultramafic rocks. Neal and Stanger 1983) suggested that low temperature, post-serpentinization redox reactions were generating the hydrogen. A similar explanation was proposed by Coveney et al. (1987) to explain high hydrogen gases along the Nemaha anticline in Kansas. Deep mantle sources for hydrogen with faults providing the conduits to the surface have also been suggested (Hawkes, 1980). Wakita et al. (1980) reported hydrogen release during fault movement, with hydrogen concentrations rising as high as 3.0% by volume compared with background values that were only 0.5 ppm (almost the same as that found in the atmosphere). They proposed that the hydrogen was generated during the faulting by reaction between water and fresh mineral surfaces. Hydrogen isotope studies by Kita et al. (1980) supported this idea.

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Figures 2 and 5 show that considerable quantities of hydrogen are present in equilibrium with deep mineral assemblages that contain no iron or other variable valence metals, and that the highest hydrogen percentage observed is in the "clean sandstone" system. Since carbon dioxide increases and methane decreases as the hydrogen content rises, it suggests the possibility that methane is being oxidized by water to give carbon dioxide and hydrogen (see Discussion below). Examination of the number of moles of these compounds in the "clean sandstone" system shows that carbon dioxide and hydrogen do in fact increase in the expected 1:4 ratio. However, oxidation of methane could not be the explanation for the high hydrogen gases described by Coveney et al. (1987) in Kansas because those gases contain only very small quantities of carbon dioxide.

Hydrogen should be a very mobile molecule in the hot subsurface and may be rapidly lost by diffusion (Hawkes, 1980). This process cannot be treated by a purely thermodynamic method in an isolated system, and a formal treatment of diffusion is beyond the scope of our paper. For shallow reservoirs (where thermodynamic equilibrium is not achieved), hydrogen could be lost by diffusion towards the surface, where it would be oxidized. Since readjustment to equilibrium does not occur under these conditions, gas composition would not be reset.

CARBON DIOXIDE

Carbon dioxide is a common component of natural gas with concentrations ranging from near zero to 100%, but all known high-purity carbon dioxide accumulations are in areas where carbonate rocks are associated with igneous activity or thermal metamorphism (Farmer, 1965). Studlick et al. (1990) described an example from the Pisgah anticline, Mississippi, where abnormally pressured, high-purity carbon dioxide originated from metamorphism of Jurassic carbonates by the Jackson Dome igneous intrusion. A similar situation occurs in the South China Sea, where carbonates are intruded by volcanics. Carbon dioxide is also generated at somewhat lower temperatures by the reaction of carbonates with clay minerals (Hutcheon et al., 1980). These observations are consistent with the thermodynamic calc lations that show the equilibrium amounts of carbon dioxide increasing with rising temperature that accompanies increasing depth of burial.

The simple thermal decomposition of calcite can be described by the reaction,

CaCO[3] = CaO + CO[2]
(Equation 1; SEE PAGE IMAGE)

but calcium oxide reacts with water to give calcium hydroxide, which is the mineral portlandite. This is

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not a very common mineral and implies that the thermal breakdown of calcite in nature is more complex and depends on other mineral species in the system. Both silica and clays may be involved. Thus it is not possible to assign a specific temperature range or depth range for the thermal breakdown of carbonates in the subsurface.

DISCUSSION

For deep gas exploration, the most important aspect of the thermodynamic calculations is predicted gas composition. Because gas composition is controlled by the rock mineralogy at any given depth, calculated changes in mineral composition are also available in the program output. For example, Table 3 shows a complete set of data for temperature/pressure pairs at 10,000-ft (3048-m) increments over the depth range 10,000-40,000 ft (3048-12,192 m) for the "silica/feldspar/iron oxides/calcite + C" system. Input data are also included.

In complex systems, it can be difficult to identify specific reactions that act to control gas composition, but in simple systems, such as our "clean sandstone" assemblage, it may be possible. Gas compositions in the figures are presented as volume percents because this is economically important. The diagrams, however, give no information on total amounts of gas and are not always useful in understanding the reactions that are occurring. For example, in the "clean sandstone + C" system, the equilibrium amount of methane (expressed as the number of moles) increases by 62.2 mole % from 10,000 to 15,000 ft (3048-4572 m), but Figure 2 shows that the methane volume percent in the gas actually decreases slightly. This happens because between 10,000 and 15,000 ft (3048 and 4572 m) hydrogen i creases slightly and carbon dioxide increases by 64.4 mole %, both of which act to dilute the methane. Table 4 shows the number of moles of methane, water, carbon dioxide, hydrogen, and graphite as a function of depth for the "clean sandstone + C" system. Graphite decreases to zero over the first 15,000 ft (4572 m) and is responsible for the large increases in methane. This conversion can be quantified by considering changes in the number of moles of each of the volatiles and then computing the ratios relative to carbon dioxide. For CH[4]/H[2]O/CO[2]/C, the relative ratios are +1.00/-2.00/+1.00/-1.98, respectively (Table 4), which is virtually identical to the values of +1/-2/+1/-2 expected for the reaction:

2C + 2H[2]O = CH[4] + CO[2]
(Equation 2; SEE PAGE IMAGE)

showing that methane can be generated by the reaction of graphite with water. In this system, graphite becomes thermodynamically unstable at quite shallow depths, but it is important to stress again that the thermodynamic calculation of gas composition is only valid when the system is in equilibrium. Equilibrium will not be achieved at 15,000 ft (4572 m), so we cannot realistically expect a graphitic residue to be converted to methane at this depth in nature. However, when a system with the "clean sandstone + C" composition is buried more than about 30,000 ft (9144 m), graphite will react with water to generate methane.

Another possible reaction that might eliminate graphite is

C + 2H[2]O = CO[2] + 2H[2]
(Equation 3; SEE PAGE IMAGE)

This does not seem to be important, however, because little hydrogen is predicted by the thermodynamic

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calculations. Table 4 shows that the moles of hydrogen generated gives a relative ratio of only 0.02, not the value of 2.0 that would be consistent with the formation of carbon dioxide and hydrogen.

After graphite is eliminated at 15,000 ft (4572 m) in the "clean sandstone + C" system, the methane content steadily decreases with depth, both as a percent of the total and in moles (Table 4). From 35,000 to 40,000 ft (10,668-12,192 m), the decrease is 0.00428 moles. Over this depth range, water decreases by 0.00855 moles, carbon dioxide increases by 0.00428 moles, and hydrogen increases by 0.01710 moles. The relative changes are -1.00/-2.00/+1.00/+4.00 for CH[4]/H[2]O/CO[2]/H[2], exactly the ratios expected for the reaction,

CH[4] + 2H[2]O = CO[2] + 4H[2]
(Equation 4; SEE PAGE IMAGE)

In the deeper part of this profile, methane is being eliminated by reaction with water to give carbon dioxide and hydrogen, and this reaction also appears to be responsible for the removal of methane in the other mineral assemblages studied.

If carbonates are present in the subsurface, they may break down with rising temperature and increasing depth of burial to produce carbon dioxide. In this paper, the simplest calcite-bearing system considered is "silica/feldspar/calcite," which has been discussed previously, both with and without graphite. Gas compositions are shown in Figures 4 and 5; the number of moles of calcite and volatiles are listed in Table 5. With increasing depth, the amount of calcite decreases slowly at first, then more rapidly; calcite is no longer stable in this system by 30,000 ft (9144 m). Carbon dioxide increases by a factor of nearly 3000 over this range. From 10,000 to 30,000 ft (3048-9144 m), calcite decreases by 0.02693 moles (Table 5) and carbon dioxide increases by 0.02874 moles, so 0.00181

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moles of carbon dioxide are not accounted for by the thermal breakdown of calcite. If this portion is compared with methane, water, and hydrogen, the ratios are -1.00/+3.64/+0.82/+4.02, suggesting that the oxidation of methane expressed by equation 4 is going on but that the situation with water is more complex, probably because of changes in hydroxl-bearing minerals. In the deeper part of the section from 35,000 to 40,000 ft (10,668-12,192 m), equation 4 describes the reaction very well with CH[4]/H[2]O/CO[2]/H[2] relative ratios of -1.01/-1.71/+1.00/+4.06, which are close to the ideal ratios.

The removal of graphite by reaction may not seem consistent with the observation that graphite occurs in some metasediments, where it clearly survived deep burial or at least high temperatures. However, thermodynamic calculations for high carbon systems show that graphite can survive to at least 40,000 ft (12,192 m). For example, we ran the "silica/feldspar/iron oxides/calcite" system with 50% of the pore space occupied by graphite (i.e., 5 vol. % of the rock). The resulting gas compositions are shown in Figure 11. Methane only decreases by about 14% from 0.01322 moles at 10,000 ft (3048 m) to 0.01139 moles at 40,000 ft (12,192 m), whereas moles of graphite hardly change over the same range. The presence of high graphite content stabilizes the methane.

Locally, high carbon contents can become associated with oil reservoirs in several ways, but most commonly they take the form of tar layers. These generally form at, or close to, the oil-water contact as a result of biodegradation, water washing, or gas deasphalting. On deep burial, the tar layers will produce a zone of reservoir rock with a significantly higher carbon content than the rest of the reservoir. Comparison of Figures 7 and 11 shows that the quantity of carbon in the rock has a dramatic influence on gas composition. In the case of a reservoir where oil was uniformly cracked to gas and a graphitic residue, the composition of the system will not vary much throughout the reservoir, and either volume A or B (Figure 12, reservoir II) could be used in calculating gas composition When a tar layer forms, the composition at the top of the reservoir (Figure 12, reservoir I, volume X) and in the vicinity of the tar (Figure 12, reservoir I, volume Y) will be quite different and will lead to very different calculated gas compositions. This raises the important question of the volume of rock that is actually effective in buffering gas composition. Unfortunately, we know of no way of answering this question effectively. However, if, on deep burial, loss of porosity through cementation were to effectively isolate the top and bottom of reservoir II (Figure 12), then methane is likely to survive near the tar mat, whereas it will be eliminated in the main part of the reservoir (volume X).

At the top of the reservoir, gas will be in contact with the seal. Seals can be formed by a wide variety of rock types including cemented silica, carbonates, shales, evaporites, tars, and even igneous rocks. This could lead to a mineral assemblage in contact with the gas that is very different from any of those discussed so far. Although the thermodynamic program can deal with any mineral assemblage for which there is thermodynamic data, at present we do not know how far the influence of the seal mineralogy extends into the reservoir. A consideration of seal mineralogy is beyond the scope of this paper, but it seems likely that reaction of gas with the seal would provide a thin "skin" of reacted minerals that are stable in contact with the gas, and that this would effectively stop fur her reaction because seals have very low permeabilities.

In the iron-bearing systems (Figures 6, 9, 10), increasing magnetite contents with depth accompany decreasing amounts of hematite, which implies that something in the system is being oxidized. The most likely candidates are graphite, hydrogen, or methane, corresponding to the three possible reactions given by equations 5-7:

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3Fe[2]O[3] + C = 2Fe[3]O[4] + CO + 2H[2]
(Equation 5; SEE PAGE IMAGE)

3Fe[2]O[3] + H[2] = 2Fe[3]O[4] + H[2]O
(Equation 6; SEE PAGE IMAGE)

6Fe[2]O[3] + CH[4] = 4Fe[3]O[4] + CO[2] + 2H[2]
(Equation 7; SEE PAGE IMAGE)

In the "silica/feldspar/iron oxides" system below 10,000 ft (3048 m), the thermodynamic calculations predict no graphite or carbon monoxide, so that the reaction described by equation 5 is not operating. Table 6 shows that between 35,000 and 40,000 ft (10,668-12,192 m), the decrease in moles of hematite and the increase in moles of magnetite are in the 3-to-2 ratio expected from equation 7. Using these data, it is possible to calculate the decrease in methane and the increases in carbon dioxide and hydrogen. The corrected values for water and the gases then have relative ratios (Table 6) that fit equation 4. Apparently, the reactions described by equations 4 and 7 are going on in parallel.

The sulfur-bearing system is the most complex studied, and many parallel reactions are possible. Hydrogen sulfide is not stable at 10,000 ft (3048 m) but increases steadily with depth and has its highest predicted concentration at 40,000 ft (12,192 m). For the iron-bearing minerals, magnetite increases with depth, and hematite and pyrite decrease. Over the depth range from 25,000 to 40,000 ft (7620-12,192 m), 1.0 mole of magnetite is formed for each mole of hematite and pyrite that is eliminated. Anhydrite increases with depth.

Thermodynamic calculations can be used to predict subsurface gas compositions at depths and temperatures only where equilibrium is reached. This depth is not well known, but it is probably below 25,000 ft (7620 m), so that there is very little available gas composition data to constrain the modeling attempts. Possible sources of information would include deeply buried reservoirs that are now shallow, and fluid inclusions in cements and overgrowths that sampled the deep burial environment.

CONCLUSIONS

Thermodynamic calculations using a free energy minimization approach show that equilibrium gas composition in the deep subsurface depends strongly on reservoir mineralogy. Calculations were carried out both with and without graphite to simulate the differences between reservoirs that were initially filled with oil but were subsequently cracked to gas, and those that originally contained just gas.

In clean sands with few accessory minerals, equilibrium methane concentration drops to zero at about 25,000 ft (7620 m), but in the presence of graphite additional methane is generated, and at 40,000 ft (12,192 m) the gas still contains nearly 10% methane. The gas is generated because graphite reacts with water to give carbon dioxide and methane. An alternative reaction that generates carbon dioxide and hydrogen does not seem to be important. When no graphite is present, the absolute amount of methane (i.e., moles of methane) drops because it is oxidized by water to give carbon dioxide and hydrogen. In high graphite systems, however, methane survives at high concentrations to the greatest depths studied.

In deep clastic reservoirs with significant amounts of calcite cement, the calcite becomes thermodynamically unstable and eventually breaks down thermally to give carbon dioxide that dilutes the methane and makes gas composition uneconomic. The details of the thermal decomposition of calcite depend on rock mineralogy, so it is not possible to specify an exact depth or temperature where this reaction becomes important. Equilibrium iron-bearing systems become more reducing with depth, and hematite decreases while magnetite increases. This

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reduction is balanced by the oxidation of methane to carbon dioxide and hydrogen. In addition, the oxidation of methane by water goes on at the same time.

Sulfur-bearing systems lead to the formation of hydrogen sulfide, but the increasing number of phases considered and the large number of possible interactions make it difficult to identify specific reactions.

Thermodynamic modeling can be a useful tool for predicting gas composition in the deep, undrilled subsurface, but it cannot be applied at shallow depths where gases have not reached thermodynamic equilibrium.