Chemical osmosis, reverse chemical osmosis, and the origin of subsurface brines

OOlb-7037/82/081431-1X$03.00/0

Geochimxrr cr Cosmochimico Ada Vol. 46. pp. 1431 10 1448 Q Pergamon Press Ltd. 1982. Printed in U.S.A.

Chemical osmosis, reverse chemical osmosis, and the origin of subsurface brines DONALD Dept. of Geology,

245 Natural (Received

History

L,. GRAF

Bldg., University

of Illinois,

1301 W. Green

July 30, 1981; accepted in revised form

St., Urbana,

Illinois

61801

April 13, 1982)

Abstract-Calculations using recently-tabulated values of density and osmotic coefficient for NaCl-Hz0 indicate that overpressuring is more than adequate to overcome chemical osmosis and drive reverse chemical osmosis in sedimentary sequences. The best-demonstrated overpressuring mechanism is the rapid deposition of fine-grained sediments. The dehydration of gypsum contributes to overpressuring for brief time intervals at shallow depths, whereas water evolved during the protracted conversion of smectite to illite is probably a subordinate, but continuing contributor to overpressuring at greater depth. Occurrences of overpressuring in sedimentary sections older than Cretaceous indicate that post-depositional mechanisms such as tectonic compression and aquathermal pressuring must also operate. The latter may be of major importance in geothermal areas with adequate low-permeability seals, and a nontrivial contributor in areas of normal geothermal gradient because of shales that sharply decrease normal fluid flow. The strongest arguments for the importance to present-day brine compositions of membrane concentration of sea-water solutes are (1) the correlation of 6D values of water molecules of pore fluid with those of local meteoric water, and (2) the need for major sources of Mg2+ and Cl- in apparently evaporitefree basins. Even where dissolution of halite is a major contributor of solute, reverse chemical osmosis still operates to leak relatively dilute water. Of the associated diagenetic chemical reactions, that of Mg*’ with limestone to form dolomite is particularly effective in generating concentrated Cl- brines rich in Ca*+. It decreases the concentration of Mg*+, increases that of Ca*+, and decreases those of both SO:- and CO:- by precipitating CaCO, and CaS04 because of the Ca2’ common-ion effect

INTRODUCTION OSMOTK behavior by shales has been proposed by a number of authors, cited in the next section of the paper, as one of the processes involved in forming the distributions of chemical composition and porefluid pressure observed in sedimentary basins. Doubts about the geologic significance of osmotic processes involve ( 1) the existence in nature of fluidpressure differences great enough to drive them, (2) the existence in nature of low-permeability beds sufficiently free of macro-porosity so that micropore flow is not short-circuited, (3) the belief that these processes act effectively upon brackish water, but cannot produce brines from sea water, (4) the belief that unrealistically large volumes of fluid would have to be pushed through low-permeability beds, and (5) the possibility that the solute content of the pore fluid might more easily be explained by ion exchange and/ or solution of halite and other evaporite minerals and/or shifting chemical equilibria between minerals and pore fluid during basin development (Carpenter, 1978; Carpenter and Trout, 1978; Lambert, 1978; Manheim and Horn, 1968). This paper addresses these concerns. There has been some confusion about the difference between osmosis and reverse osmosis. The principles involved are summarized in Appendix I. Differences in electrical potential and temperature on the two sides of a shale, as well as differences in chemical concentration, will result in fluid flow and a fluid pressure difference (e.g., see DeGroot and Mazur, 1962; Katchalsky and Curran, 1967; Gro1431

enevelt and Bolt, 1969; Haase, 1969). The electrical and thermal osmotic effects are ignored in this paper, principally because they have not been experimentally studied at diagenetic temperatures and pressures, but also because they appear likely in most stratigraphic sections to be small relative to the chemical osmotic effects. Many brine analyses, measured as mg/l, have been reported in the literature as ppm, as noted by Graf et al. (1966) and Carpenter (1978). Wherever possible, the unambiguous units of mg/l or g solute/ 10’ g solution are used in this paper. CHEMICAL

OSMOSIS

McKelvey (quoted in Jones, 1969b) generated osmotic pressures within 95% of theoretical when he placed salt solutions of various concentrations in contact with plugs of Wyoming bentonite. Kemper ( 196 1) obtained fair agreement when he carried out similar experiments using shales and compacted-clay membranes. Stratigraphic sections that contain both shales and evaporite units are the most obvious sites for chemical osmosis to occur in nature. Berry (1959) interpreted closed-low potentiometric surfaces in the Cretaceous aquifers of the San Juan Basin in northwestern New Mexico as resulting from downward-directed osmotic withdrawal. The Paradox Member of the Hermosa Foundation, of Pennsylvanian age, contains evaporite facies. Hanshaw and Hill (1969) suggested that the very high potentiometric surface in several Upper Paleozoic aquifers in this area and the exis-

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D. L. GRAF

maining behind the membrane (White et ut., 1963; White, 1965): increased salinity, increased Ca”+ cation fraction relative to that of Na+, ioss of CO2 species and B species, etc. Uncharged species such as H3B03, H2S, H2C03, and NaHC03, which are minor to abundant in solutions of near-neutral pH, should pass easily through micropores and, of course, even a complex such as NaSO; presents a much lower surface charge density than 2Na+ + SOi-

FIG. 1. Distribution of subsurface brine compositions from a stratigraphic interval in the Upper Mississippian section of the Illinois Basin (Fig. 3 of Graf et al., 1966, reproduced by permission). The outcrop belt of these formations (subcrop where under the Pennsylvanian) is shown in black. The closed dashed line is the isoconcentration contour for 130,000 mgfl salinity, and the depression contour outlines the deepest part of the Basin in Illinois. Samples with Ca’+ cation equivalent fractions greater than 0.11 are shown as pluses. Regions A, B, and C have different salinity vs. depth trends.

tence of a potentiometric

gradient into southeast Utah three to five times the regional average marked these units as the outflow from the San Juan mem-

brane system. Marine (1974) calculated that the slight overpressurings observed for two wells from a buried Triassic basin in South Carolina matched the osmotic pressures that should result from the salinity differences. The ~tentiometric low in the Viking Sandstone of Lower Cretaceous age in central Alberta cannot be expIained by gravitatjonal Aow of water (Hanshaw, 1972) but must result from osmotic cross-formational withdrawal of water through the shale of the Joli Fou Formation into more saline underlying units. REVERSE CHEMICAL OSMOSIS It is this process, rather than chemical osmosis, that has aroused most controversy. The invoking of reverse chemical osmosis to help explain observed subsurface distributions of chemical composition and fluid pressure predated systematic laboratory experimentation on compacted-clay systems. Berry (1969) summarized such literature from the 1930’s onward. Evaluation of a large number of subsurface water compositions in the light of known processes that might affect chemical composition led to a set of postulated changes that shale-membrane filtration must be bringing about in the fluid re-

Field studies in the Illinois Basin and the western Canada sedimentary basin have supported the operation of reverse chemical osmosis. The hydrologic model of Bredehoeft et af. f 1963, 1964) incorporated shale membrane f&ration as a major element and succeeded in matching the lateral salinity profiles found in typical Illinois Basin aquifers. The model set cross-formational gow into the aquifer of interest from below at zero, and did not consider the osmotic pressure that would have to h overcome. Craf ei nf. ( 1966) showed that the rate of salinity increase with depth for pore fluids from an interval in the Upper Mississippian section of the Illinois Basin decreased near the structural low of these beds, and that the CaZ+/NaC increase with depth reversed itself there, behavior consistent with relatively less saline, Nat-rich fluid moving upward across bedding into this interval (their Fig. 3 is reproduced here as Fig. f ). Clayton er al. ( 1966) found that the 60 values of waters extracted from pore fluids of marine rocks from Texas, Michigan, Alberta, and the fllinois Basin matched in each area the value for local meteoric water. These authors concluded that there had been expulsion of water molecules of the original sea-water pore tilling but with substantial retention of dissolved solids. By comparing 6D values of pairs of samples on the Iowhydraulic-potential and high-hydraulic-potential sides of shales at particular localities, hence with the same meteoric water input, Graf et ai. (1965) in the Illinois Basin and Hitchon and Friedman (1969) in the Alberta Basin were able to show that the eatrent from cross-formational Bow is isotopically lighter, a small effect observed earlier by chemists in non-geological systems. With the evidence of mechanism afforded by Clayton et nl. (1966), Graf et ai. (1966) were then able to reproduce observed pore-fluid compositions in the Illinois Basin with a model involving dolomite and chlorite formation concurrent with shale membrane filtration of a small number of pore volumes of sea water and fresh water, bacterial reduction of SOi-, and membrane leakage of NaHCO>. The only evaporite minerals observed thus far in Illinois Basin rocks are scattered occurrences of anhydrite too minor in amount to register on down-hole geophysical logs (Stevenson et al., 1975) but the pore-volume estimates at Graf et al. (1966) are still in principle somewhat high because they ignore pore fluidmineral interactions, The estimates, on the other hand, are low because they assume perfect membrane efficiency. Hitchon and Friedman (1969), working with excellent sets of porosity, brine-salinity, and brine-deuterium-content measurements and lithologic descriptions, made basin-wide mass-balance calculations for deuterium and dissolved-solids contents of pore fluids of the western Canada sedimentary basin. These brine compositions can be derived by saltfiltering the original sea-water pore filling plus about 2.9 pore volumes of fresh water, dissolving some NaCl from the sedimentary rocks of the basin, and.redistributing these dissolved solids. Halite solution is considered of subordinate importance as a source of dissolved solids; evaporites comprise only 5.7% of the rocks of the basin, and nearly 75% of them arc concentrated in the Middle Devonian (Hitchon

CHEMICAL

an underlying overpressured sequence, in which the degree of overpressuring increases with depth (Fowler, 1970). There is a marked drop in hydraulic head from the lower to the upper side of the shale, the pore fluid just above the shale is the least saline found in the normally-pressured interval, and the pore fluid just below the shale has an enhanced salinity which decreases gradually with depth in the porous unit below the shale. The same pattern of pressures and salinities is repeated to a lesser degree across thinner shales in the overpressured sequence. A regional fault and a number of minor faults cut the area, but they appear not to have carried enough of the fluid flow to dominate over reverse chemical osmotic transport across shales. The gradual decrease of salinity with depth in a single porous zone in the overpressured region was attributed by Fowler (1970) to redistribution by ionic diffusion along the concentration gradient between the highly saline fluid left under the capping shale and the less saline fluid transmitted by the underlying shale. Mangelsdorf et al. (1970) discussed the ion fluxes from gravitational settling and from diffusion on the thermal gradient (Soret effect) that must also contribute to this redistribution. Considering a large body of oil-field data on lithology, fluid pressure, and pore-fluid composition for the Northern Gulf of Mexico Basin within which the Chocolate Bayou Field lies, Jones (1969a) reported large differences in salinity across clay beds only a few tens of feet thick, the less saline fluid being above the bed, especially when the bed lies at the top of an overpressured zone. One might suspect, from the presence of both bedded salt and salt diapirs in the U.S.A. Gulf Coast, that halite would be the dominant source of dissolved solids in pore fluids there. But subsurface flow patterns are complicated by faulting and by permeability differences among depositional facies. Kharaka et al. (1977) concluded from Br/CI measurements that dissolved halite contributes significantly to pore-fluid compositions observed in fields sampled in the Houston-Galveston area, but not in the Corpus Christi area. These authors reported that salinity and ion-ratio changes,

et al., 1971). Shale membrane efficiency emerges from the mass-balance calculations as only 25% or a little better, but the combined operation of a succession of shales is believed to have retained substantially all solutes of sea water and freshwater within the basin, but not many water molecules from sea water. Loewengart (1962) had earlier pointed out that dolomitization not only increases the Cal+ content of brines but also decreases the SO:- content by forcing anhydrite precipitation (see also Zak, 1980). Evaporite-mineral assemblages that must have formed from such MgS04-deficient solutions have been found at quite a number of localities (Braitsch, 197 1). One of these is a 33,700 km’ ( 13,000 mi*) area of the Late Silurian Salina Group in the Michigan Basin, which contains as much as 30 m (100 ft) of sylvitebearing halite (Matthews and Egleson, 1974). The brines of the stratigraphically higher Detroit River Group (Middle Devonian) contain extremely high concentrations of CaCI, (Sorensen and Segall, 1974). A striking feature of these brines, analyses of which are plotted in Fig. 2 together with those of the brines of Graf et al. (1966) from Illinois and Michigan, is that beyond a certain salinity there is a sharp drop in the absolute concentration of NaCl even though those of CaCI,, MgCI,, and KC1 continue to rise. Braitsch ( 197 1) discussed post-depositional marine brine histories that could lead to halite precipitation. The IOO- to 150-m thick beds of tachyhydrite, CaMg,CI, - 12 H,O, and tachyhydrite plus bischofite, MgCl, * 6 H,O, that occur in Cretaceous basins of Brazil and West Africa (Belmonte ef al., 1965; Fernandes, 1966; Wardlaw, 1972) indicate that it must also be possible to form Cl- brines with a high Mg2+/ Ca*+ ratio.

U.S.A.

Gulf Coast

The Tertiary section from which the Chocolate Bayou oil field produces in Brazoria County, Texas, consists of a normally-pressured interval separated by a shale unit from I

I

I

1433

OSMOSIS

I

I

I

I

I

.

. :.a . .

a.

a* .-

* * PI

k, t I I

0

..

-_ I

l

*

4%

I

I

1 Total

I

2 Chlorides,(mg/l)

I

I

3

I

I

4

x 10m5

FIG. 2. Content of CaQ (solid dots) and NaCl (stars) versus total salinity for the subsurface brines from Michigan described by Sorensen and Segall (1974) and those of Graf et al. (1966) for which salinity is greater than 20,000 mg/l and separate analyses for Na+ and K+ are available. Analyzed values for Na+, KC, Ca*+, and Mg ‘+ have been converted to chlorides, ignoring the small amounts of HCO; and SO:- present. Point distributions for MgC12 and KC1 parallel that for CaCl* at successively lower concentrations.

1434

D. L. GRAF

for six pairs of fluid samples on opposite sides of shales capping overpressured xones, are those expectable for membrane filtration. Maximum filtration efficiency is 30%.

But the water table lies at some point within the thick capping shale, so there is presumably plug flow through this micropore network, and, as noted by White (f968), the large shift in 60 of the brine that should result from continued evaporation is not observed. The shift to be expected Central Valley of California from membrane filtration is slight (Graf et al., 1965; HitBerry (1973) discussed anomalous fluid potentials be- chon and Friedman, 1969; Coplen and Hanshaw, 1973). One wouId like to use the relative membrane retention of lieved to exist in California in thick Franciscan and Great Br- as a further test of whether the ~~ntration of solutes Valley mudstones of Jurassic-Cretaceous age throughout a fault-bounded region 645-805 km long by 42-129 km from Colorado River water took place by evaporation or membrane filtration, but White (1965) could find no clear wide. He considered compression of this block, probably trend for this ion. still occurring, to be responsible for the general overpresThe large total heat flow requires brine convection in the suring in the mudstones as well as for postulated diapiric porous sands beneath the capping shale (Elder. 1965; shale intrusion into the near-surface Kettlemen folds, creHelgeson, 1968b), but it is not possible from available litating local overpressured regions there. Overpressuring erature to decide what degree of fluid overpressuring is from the original rapid deposition of 15.2- 18.3 km of mudmaintained The accumulated experience in the New Zeastones and siltstones was a~~owl~g~ in this paper, but land geothermal region (Ellis and Mahon, 1977) suggests considered to have dissipated, in part because normallythat macrochannels are plugged by silica and carbonate pressured sections of these rocks are observed throughout precipitation, an interval of about 10’ years foil6ws in which large areas outside the geopressured region. In contrast, fluid reservoir temperature builds up (and membrane filKharaka and Berry (1973) argued for longer persistence of the de~it~ona~ overpr~suring effect in this region be- tration would be feasible), and then tectonic activity creates new macrochannels through which there is substantial outcause of the relatively long period of continuous sedimenflow for a few thousand years. Helgeson (1968b) cited artation of materials with low hydraulic conductivities, and ticles from 1855 describing spectacular thermal spring and because the resulting section of this material is thick enough geyser activity in the Salton Sea area, in contrast to the so that clay mineral dehydration in its lower portion might lack of such features today. help sustain the overpressu~ng, The published evidence discussed in this section cannot be said to demonstrate shale membrane behavior in any Salton Sea geothermal area geothermal area. However, the question ought to be considered open until a thorough evaluation can be made of Chloride brines containing up to 260,000 ppm total disdata obtained in the geothermal exploration program of the solved &ids, with Na~~Ca~l~:K~~MgCI* approximately 3.55:1.95:1:0.0038 by weight are found in the Imperial last decade. Hemley’s suggestion (in Helgeson, 1968b) that Valley of southern California under a 0.61-0.91 km (ZOOO- the temperature gradient across the shale in the Salton Sea area may be great enough for significant thermoosmotic 3000 ft.) shale cap at temperatures from 300’ to 360’C flow should be evaluated. (Helgeson, 1968& Muffler and White, 1969). Recent deltaic sediments extend to at least 4,270 m (14,000 ft) depth (White, 1968). and the described evaporite units consist of Experimental studies a playa gypsum deposit and of beds of thenardite, miraThe existence of reverse osmotic behavior by compacted bilite, and bl&fite intercalated in a lacustrine sequence clays has been well demonstrated in laboratory experiments, (Sampson and Tucker, 1942; Dibblee, 1954). The bD content of the water of the brines rules out a but not studied over the futl range of conditions of interest seawater source; Craig (1966) argued for local precipitation in nature. The work of McKelvey and Mime (1962) Milne in the Chocolate Mountains to the east. He noted that the et al. (1964), Kemper and Maasland (1964) von Engelratio of the fractional increase in dissolved chloride atoms hardt and Gaida (1963), Dirksen f 1969), Olsen ( 1969, to increase in O’s atoms remains almost constant as this 1972), Kharaka and Berry (1973) and Hanshaw and Coplen (1973) demonstrated at room temperature that ion input water increases in salinity, so that the soluble salts filtration takes place and that the associated differences in would have to come from sediments that are hot enough for thoroughgoing reaction to take place. Helgeson’s ( 1967) solute activity, temperature, and electrical potential across calculations for reaction of detrital K-feldspar to form K- the membrane are those theoretically expectable for the mica, chlorite and quartz involve significant loss of Mg*+ osmotic behavior observed. Hanshaw and Coplen (1973) from solution and gain of K+ by the solution. consideration forced NaCl solutions through bentonite, ihite and montof the wider system including Ca2+ and Na+ suggests a morillonite membranes at room temperature, and obtained possible loss of the latter and gain of the former-to the fair agreement between observed and calculated effluent concentrations. Kharaka and Berry ( 1973) determined the solution. The chloride nresumablv wouId be derived from solid solution in sedimentary minerals, intergranular films, relative retardation of ten cations and six anions in solutions and scattered grains of halite. The problem of solute con- forced through membranes of illite, bentonite, and disagcentration in the Salton Sea area would be moderately im- gregated shale at temperatures from 20 to 70% Coplen proved if Colorado River water could be taken as the input. and Hanshaw ( 1973) verified the existence of the postulated The &/Cl ratio of the brines is much too low to permit membrane fractionation effects for the stable isotopes of direct involvement of seawater; Berry (1966) noted that it hydrogen and oxygen. Kharaka and Smalley (1976) forced chloride solutions, containing nine cations at total-dishas the value of near-surface meteoric water of the area (and thus of Colorado River water). He argued further that solved-solids levels up to 6370 mg/i, through bentonite and the value of the ratio rules out the pussibility of hitherto kaolinite layers at several hydraulic gradients and temperunr~gni~ evaporites at depth being diifved, but White atures up to 8YC. The sequence of cation retardation was (1968) pointed out that compIete evaporation of Colorado determined, and the relative filtration ratios of Nat and River water or of early-stage marine evaporites would yield Ca*+ appear to reverse at very low flow rates to give the the proper ratio. relative retardation of Ca2+ postulated in earlier field studElder (1965) stated that the principal method of heat ies (see also Kharaka, 1973). flow discharge for land thermal areas is flashing or evapBenxel and Graf ( 198 1f found that at room temperature oration at the water table, and Craig (1966) and Helgeson salt filtration efficiency of a smectite membrane with clay (1967) suggcwted this as a process that would accomplish Rakes in reasonably parallei orientation was roughly double the solute concentration required for the Salton Sea brines. that for one with jumbled (“card-house”) fabric. Graf P/

CHEMICAL

1435

OSMOSIS

al. ( 198 1) observed that the gradual dewatering of a smectite membrane with temperature altered its behavior so that the retention of Ca*+ increased with temperature and above about 160” became greater than that for Na+. The experiments of the latter authors used a compaction pressure equivalent to that of a 1.6-km (1-mi) depth of burial and a brine 5.06 molal in NaCl and 0.45 molal in CaCl,

2

Depth,am

6 14

(257,000 g solute/lO” g solution), and salt filtering efficiency at 95” and 140°C was about 20%. The loss of efficiency from increase in salinity is partly compensated for by the decrease of pore diameter with depth of burial. Salt filtration by shales in nature should still be significant at high salinities, particularly if there are multiple shales as in the area studied by Hitchon and Friedman (1969). This summary is illustrative rather than exhaustive; there is extensive additional literature of potential applicability in soil physics, biophysics, desalination engineering, and civil engineering. Depth, ft/lOOO FLUID

PRESSURE

CALCULATIONS

The most discussed mechanisms for generating overpressuring are (1) rapid sedimentation of finegrained materials, (2) lateral tectonic compression, (3) aquathermal pressuring (Barker, 1972), and (4) dehydration of gypsum and/or clay minerals. The maximum values of some of the pressures involved, based upon calculations that assume instantaneous pressure changes and therefore ignore dissipation effects, are given in this section, before discussing the geological duration of the several generating mechanisms. Consider first a vertical section through normally-pressured sedimentary rocks extending to 7.620-km (25,000-ft) depth, with a mean surface temperature of 12°C and a thermal gradient of 30”C/km, about in the middle of the 22 to 36” C/km range reported for the Gulf Coast by Heard and Rubey (1966). Density of the brine-saturated sedimentary rock is 2.2 g/cm3 down to 1.524 km (5,000 ft), 2.3 from 1.524 to 3.048 km (10,000 ft), 2.4 from 3.048 to 4.572 km (15,000 ft), and 2.5 below 4.572 km, an approximation of the density versus depth relation adopted by Nettleton (1934) for the U.S.A. Gulf Coast. In this initial model, salinity increases at a constant rate of 14,025 g NaCl/106g HZ0 per 0.305 km (1,000 ft), reaching a value at 7.620 km (25,000-ft) depth that is 98% of saturation with halite at 25°C (Rard and Miller, 1979) but only about 70% of that (Clark, 1966 citing Keevil, 1942) at the model temperature of 240°C for that depth. Dickey (1969) reported higher salinity gradients, the most frequently measured values lying between 25,000 and 75,000 mg/l per 0.305 km (1000 ft), but these are over relatively short vertical intervals and their extrapolation to the full depth range of the model is unrealistic. Converting his gradients to a weight/weight basis would increase them by as much as 25% for the most concentrated solutions. Taking Nat to be the only cation in solution is most appropriate for regions where there is significant dissolution of halite, least so for NaCl-free sections where salinity results from salt filtration and wallrock reaction. But even in the latter cases, the hoped-for gain in accuracy of calculated density and chemical osmotic pressure values from recognizing CaCl,, MgCl,, and KC1 contents would not be achieved because of the poorer quality of data available for these systems. For the vertical variations in temperature and NaCl content assumed above, the decrease in density of pore fluid with depth because of the former turns out to be almost exactly compensated for by the density increase because of the latter. Because of the weak resultant dependence of solution density upon his pair of variables, it is satisfactory

FIG. 3. Calculated values of pressure (a) lithostatic pressure; (b) hydrostatic of effective pressure (70% of lithostatic (d) osmotic pressure.

change with depth: pressure; (c) 70% minus hydrostatic);

to break the section down into ten 0.762-km (2500-ft) blocks, each having throughout the temperature and porefluid salinity appropriate for its midpoint, and to calculate the various quantities of interest at each midpoint. Lithostatic pressure versus depth is given by curve “a” of Fig. 3, and hydrostatic pressure by curve “b”. The latter values were obtained by using the tables of Phillips et al. (1981) (see Appendix II). The maximum amount by which hydrostatic pressure could be increased at a particular depth if the pore fluid were sealed off and forced to sustain the weight of the overlying rock column (“overpressuring,” “effective pressure”) is the difference between hydrostatic and lithostatic pressures at that point. Curve “c” shows 70% of effective pressure, an extent of overpressuring more commonly achieved than the 100% value. This is the fluid pressure differential that would act upwards across a capping shale in opposition to a downward-directed chemical osmotic pressure, assuming the uniform salinity increase with depth described above for the model.

Chemical

osmotic

pressure

Details of the osmotic pressure calculations are given in Appendix I, and the calculated values appear as curve “d” in Fig. 3. The 70%-of-effective-pressure value at any depth is 1.7 to 2.4 times the osmotic pressure, so that the former is clearly adequate to drive salt filtration. Because of the choice of standard state, the comparison between the two curves along a selected ordinate is for the extreme case in which the topmost brine in an overpressured section is in osmotic equilibrium with normally-pressured, (essentially) fresh water superjacent to an intervening shale membrane. The more probable case would be that the two pore fluids are both within the overpressured section and differ less dramatically from each other in both salinity and fluid pressure, for which the difference between comparisons along two nearby ordinates would be appropriate. The slope of the 70%-of-maximum-effective pressure curve is everywhere steeper than that of the osmotic pressure curve, so that there will be a net upward pressure driving salt filtration at points within the overpres-

D. L. GRAF

1436

8 d0 a 4 20

I 0

5

15 10 &+I%, trriooo

10

25

FIG. 4. Calculated values of pressure change with depth: (c) typical overpressuring = 70% of effective pressure (7096 of lithostatic minus hydrostatic); (d) osmotic pressure; (e) fluid pressure increase from increasing thermal gradient below 3.048&n (lO,OOO-ft) depth, assuming constant pore volume (see text); (f) fluid pressure decrease during the heating described in (e), because of thermal expansion of enclosing rock, (g) resultant of(e) and (f); (h) contribution to fluid pressure distribution from an assumed topographic relief (see text). sured region. This double comparison is valid whatever the vertical separation of the two pore fluids being considered, if the X%-of-effective-pressure curve is modified according to the degree of ovetpressuring at particular depths, e.g., dropped to zero in normally-pressured regions.

The term “aquathermal pressuring” was coined by Barker (19’72) to describe the a~itional increment in pore-fluid pressure that results if an isolated fluid volume is moved downward in a geothermal gradient, as compared with the pressure effect if the transported fluid volume is connected to the larger hydrologic system. The comparison involved following an isodensity line and a line of constant geothermal gradient, respectively, on a P-T plot for liquid water. Barker found from a parallel calculation that the aquathermal pressuring for a 30% NaCl solution was less than that for pure water. Magara ( f975a) noted that if the shale expanded, the observed pore fluid pressure increase would be less. These two effects are explicitly considered in the calculation that follows. Hydrostatic pressures for a normally-pressured section with a thermal gradient of 22Yfkm are found to differ only trivial@ from those of curve “b” of Fig. 3. A shale is then inserted at 3.048-km (iO,OOO-ft) depth as a barrier to the flow of heat and fluid, and the thermal gradient below that point is raised i~ant#~usIy to 3O*C/km. This amounts to treating a time interval, between the onset and decay of the thermal event, during which the system is considered to be at steady state. If tbc rock mass is taken to be rigid, so that pore volume remains constant, the fluid Pressure increase at constant salinity (molality) and density can be calculated using the tables of Phillips sf al. ( 1981) (see Appendix II). These increases are given as curve “e” of Fig. 4, which also shows curve “d” of osmotic pressure repeated from Fig. 3. The increased fluid pressure is still

well below lith~tatic, so that pore fluid exerts no net force upon the enclosing rock. However, the rock does experience thermal expansion, which is computed here as the volume-weighty average for the minerals of an h~t~ti~l average ~~e~tary rock. Pore volume thus encompasses everything from connected pores to isolated pores to the volumes of atomic misfit along grain boundaries. Tbe assumption is convenient because granular rearrangement consequent on temperature and pressure changes can then be ignored, but it is a nontrivial one. Norton and Knapp (X977), for example, found that unconnected porosity in fractured Sherman granite was more than 90% of total porosity. But salt filtration takes place over a much greater time span than the experiments of these authors, so that there will be at least partial compensation because of transport of these “sealed” materials by dilIusion along grain boundaries, as we11as pore redefinition in many rocks by pore-fluid dissolution and precipitation processes. A simplified version of Garrels and Mackenzie’s (1971, p. 245) mineralogical average for sedimentary rocks, modified with an eye to readily available thermal expansion data, involves (in wt. Percent) 6% albite, 6% K-feldspar, 4% hematite, 35% quartz, 11%calcite, 27% muscovite, and 10% chlorite. Molar volumes needed for conversion to volume percent are given by Robie and Bethke (1966). Volume thermal expansion values for aft but the last two~minerals are listed in Skinner ( 1966). The linear thermal expansion coefficients cited by McKinstry (1964) for muscovite and chlorite have been converted to volume coefficients by comparing unit-cell volumes computed at each temperature of interest. In considering the physical consequences for the rock column of this postulated temperature increase, attention is focused on lim~tones and s~stones. The physical state of uncemented shales under these conditions is difficult tu specify-even in “normally-pr~su~ sections, part of the weight of the overlying rock column may be borne by water that is byd~gen-Andy to clay-particle surfaces. Magara (1974), among others, has discussed non-uniform porosity and pore-fluid salinity distributions within shale units. The simplest physical assumption is that the limestones and sandstones will expand uniformly without developing planar failures, so that the pores will increase in volume by the same percentage. The resulting decrease in fluid pressure at constant temperature and safinity (rno~li~y) can bc obtained from the tables of Phillips et ai. (19gl) (see Appendix II), and is plotted as curve “f I’ in Fig. 4. The increase in fluid pressure with temperature at constant volume and safinity was calculated above (curve “e”). If the small effects described by curves “e” and “f’ are taken to be independent and therefore additive, the net effect is given by curve “g.” The latter has a steeper slope than curve “d” (chemical osmotic pressure) and wilf intersect it at a depth somewhat greater than 25,000 ft (7.620 km). For the assumed thermal gradient increase, a very thick overpressured region below a capping shale would be required if aquatherma1 pressuring were to be a major factor in driving reverse chemical osmosis. If the rock were under a large enough confining pressure, i.e., thick enough overlying section, so that the specified temperature increase caused cohesive strength to be exceeded, the rock would fail and move differentialfy along fractures into volume occupied by fluid to produce an effect oppasite in kind from that-of curve “f.” The most extreme conditions of the model. 2WC and 175 MPa (25.400 psi) lithostatic pressure, secrn inadequate, even illoking ‘for some lowering of rock strength because of the high salinity of the brine, an effect observed in laboratory sttidies. In experimental deformation of brittle rocks with pore-fluid pressures a large fraction of confining pressure, the development of microfractures begins at a fraction of the stress required for rock failure by macroscopic fracture (Brace, I971). These microfractures increase pore volume (“dilat-

CHEMICAL ancy”) and can be viewed as an alternate means of distributing some of the volume increase assigned entirely to pore-diameter increase in the calculation of the preceding paragraph. These simplistic calculations have considered aquathermal pressuring because of low-permeability beds that block fluid flow in sedimentary basins that lie in regions of normal heat flow. It is a nontrivial contributor to overpressuring, but inadequate by itself to drive salt filtration in sections where salinity increases downward at rates like that postulated by the model. Geothermal areas are an entirely different question; the thermal gradient across the capping shale in the Salton Sea area is ten times the average gradient of the U.S.A. Gulf Coast. Microfracturing The question arises as to whether effective pore diameter will be sufficiently increased by microfracturing so that salt filtering cannot take place. A key parameter involved is rock permeability, and it is reassuring that laboratory measurements, in situ measurements, and inferred values of this quantity for argillaceous rocks agree within a factor of about ten (Brace, 1981). Uncemented shales, not surprisingly, do not follow brittle deformation behavior, but instead (Mogi, 1966, cited in Brace, 1971; Brace, 1981) there is a rather uniform collapse of pores without formation of discrete fractures. The mean separation between individual clay flakes will be increased trivially in forming this dense, high-pressure slurry, and it should retain membrane behavior. The readiness with which such units flow into well bores when penetrated is in agreement with this physical description. As one proceeds upward in a thick shale capping an overpressured zone, clay-flake separation will be gradually diminished as the full effective pressure gradually asserts itself, so that the upper portion of that unit should be even more effective as a membrane. The microfractures formed in brittle rocks are typically fractions of a millimeter long and 10 grn or less in width, when measured at room temperature and pressure after an experimental run (Brace, 197 1). In spite of their apparent lack of continuity, they increase permeability measurably, but this crack permeability can be reduced by about two orders of magnitude if an effective pressure of 35 MPa (5,080 psi) is applied (Bauer and Johnson, 1979). Overpressured sections may include lithologically intermediate rocks, e.g., argillaceous limestones, that deform in brittle fashion but have an enhanced surface charge along microfractures because of clay minerals. One can estimate a maximum crack wall-separation (pore diameter), at which there will be reduced but still significant salt filtering, by obtaining the dielectric constant of water from the fit of Bradley and Pitzer (1979), calculating the distance from the wall of the center of gravity of the space charge using

1437

OSMOSIS

Gouy theory (van Olphen, 1977, Appendix III), and then, at each wall, tripling this value and adding a 5 8, Stern layer. Calculating the distance from the wall at which an exponentially declining space charge will be effective in blocking ion flow along the pore is a difficult undertaking, if even possible. The arbitrary tripling would seem to err in favor of a toothick zone of blockage. It yields critical crack-wall separations of 1.5 pm for the model solution at 7.620km (25,000-ft) depth, 3.3 pm for that at 0.762-km (2,500-ft) depth. Microfractures in the subsurface will close to widths less than those mentioned above, depending upon how much less effective pressure is than 100% of its maximum value. It appears, therefore, that the question of whether salt filtration ability is retained along the full length of mirocracks is indeterminate. Certainly it must be retained near crack terminations and across bridges to neighboring microcracks. Fluid reservoir

loss to release overpressuring

It can be argued that the chemical signatures of shale membrane flow existing in an overpressured zone (e.g., Fowler, 1970) should still be recognizable after the additional fluid loss associated with subsequent decay of overpressuring. They must also, of course, withstand a probable subsequent exchange of marine water molecules with those of meteoric water, as well as possible change by reaction with wall rocks, a subject that is considered in a later section of the paper. If membrane filtration continues to operate during the decay of overpressuring, the chemical signatures will obviously be enhanced. If the decay occurs by loss through macroporosity, the effluent should have the same chemical composition as the residue, except that the upper portion of a vertical fluid concentration gradient under a shale may be drained preferentially. Even in that case, there may be portions of the overpressured unit laterally removed from zones of macroporosity and therefore less affected. The percentage of pore fluid volume that must be leaked to reduce pore-fluid pressure to hydrostatic will vary according to how much compaction occurs in the overpressured region during pressure reduction. For the limiting case in which pore volume (and temperature) remain constant, admittedly an unlikely geological situation, the percentage can be calculated. Curve “a” of Fig. 5 assumes hydrostatic pressure in the overpressured zone to have reached lithostatic and the leaked fluid to have the chemical composition of the fluid reservoir from which it escaped, i.e., there is no salt filtration. The calculation uses the tables of Phillips et al. (1981). In this case, the percentage of pore fluid volume leaked is, of course, the same as percentage of the mass of the fluid reservoir leaked (see Appendix II). In the other extreme, if salt filtration operates and is taken to be 100% efficient, the hydrostatic pressure attained will be that for an enhanced vertical salinity gradient, and the pure water that escapes will be a lesser mass

1438

D. L. GRAF Depth, km

Depth, ft 11000

FIG. 5. Percentage of pore fluid that must be leaked to reduce pore-fluid pressure from lithostatic to hydrostatic, assuming rigid rock framework: (a) if leaked fluid has composition of brine at that depth; (b) if leaked fluid is pure water. percentage of the fluid reservoir. Results of this sort are plotted as curve “b” of Fig. 5 (see Appendix II). The maximum loss shown in Fig. 5 is about 6%. Elevation

of recharge areas

T&h (1979, 1980) argued that elevation differences of the land surface (more precisely, of the water table) act through a hydraulically continuous path to produce somewhat damped but similar surfaces of hydraulic potential deep in sedimentary basins. But Manheim and Horn (1968) concluded that past topographic relief could never have been great enough during the geologic lifetime of Atlantic Coastal Plain sedimentary rocks to drive salt filtration. Likewise, Berry (1973) considered recharge to be inadequate to explain high fluid potentials observed in the Coast Ranges and the west side of the Central Valley, California. If aquifers throughout the model section are considered to have continuity to outcrops at which they are recharged, geologically older formations outcropping at successively higher elevations, an estimate can be made of the possible topographic contribution to fluid pressure differences in the model section (curve “h” of Fig. 4). Each aquifer is assumed to have the salinity distribution with depth of the model section, and the additional fluid column above the elevation of the top of the model section is pure water at I S’C. The height of this additional column varies linearly from 0.9 14 km (3000 ft) for the stratigraphic horizon encountered at the bottom of the model section to zero for that at the top. The fluid pressure exerted by the 0.914-km column of water corresponds to the osmotic pressure of a pore fluid having 86,000 g NaCI/ 1O6 g solution. The slope of curve “h” is everywhere less than that of curve “d”, the osmotic pressure curve in Fig. 4, so that plausible elevations of recharge areas are not adequate to drive reverse chemical osmosis. Mineral

dehydration

The most important reactions for creating pressure are the dehydration of gypsum and of smectite. In

each case, the consequences might in principle differ somewhat depending upon whether the hydrate is assumed to be mixed with a great enough proportion of other sedimentary minerals so that the rock will remain rigid after dehydration, or whether it will disaggregate, compact, and expel virtually all of the newly-released fluid. The conversion of gypsum to anhydrite plus two molecules of liquid water represents an increase of about 10% in the molar volume of the assemblage (Robie and Bethke, 1966; Kennedy and Holser, 1966). An hypothetical instantaneous dehydration of a gypsum bed would therefore drive fluid pressure far above lithostatic, and would be relieved first by elevation of the overlying rock column and more gradually by flow of water into progressively more distant beds above and below. However, the amount of CaSO, is usually small (it is not even part of Garrels and Mackenzie’s ( 197 1) normative sedimentary rock), although there are obviously basins in which this generalization does not hold. In most cases, it will make little difference in the pore fluid pressure obtained whether the released water is distributed throughout the pores of a section that includes the CaSO, bed, or the CaSO, bed is assumed to compact to very low porosity. Gypsum dehydration is a simple reaction that takes place over a limited temperature range characteristic for the aHlO and salinity values of the pore fluid with which it is in contact (Graf and Anderson, 1981). Limited temperature range corresponds to brief time interval in a basin undergoing active sedimentation. The geological significance of gypsum dehydration depends upon how long it takes to dissipate the fluid pressure induced by the water pulse, a subject considered in a following section. The sign of the volume change on simple dehydration of smectite is uncertain, Anderson and Low ( 1958) and Martin (1962) having come to opposite conclusions. The geologically important reaction, however, is the conversion of smectite to illite through a series of mixed-layered intermediates (Reynolds and Hower. 1970). This reaction involves changes not only in the amount of interlayer water but also in ions such as K+ and Si’+ (Hower ef al., 1976: Boles and Franks, 1979). and the volume change for it is also unknown. Perry and Hower (1972) calculated that the conversion of interlayered I:S::25:75, making up 7.5% of a clay-rich shale, to I:S::80:20 would release 15.5 volume% water. This is a larger volume release than for gypsum dehydration, and smectite is a more common sedimentary mineral which makes up 3% of Garrels and Mackenzie’s ( 197 I ) normative sedimentary rock and is a good deal more abundant in some depositional sequences. The potential for overpressuring if the released water is expelled by subsequent shale compaction is substantial, but dehydration rates still must be considered.

CHEMICAL DURATION

OF OVERPRESSURING

To be geologically important, a mechanism for producing overpressuring must operate over considerable areas or long time spans, preferably both. Estimates of the duration of individual geologic events that drive the process are most readily available from magnetic-reversal dating in oceanic areas. Analogous estimates within continents require more subtle evaluation of local geologic history, and are more open to dispute. Aquathermal

pressuring

High thermal gradients resulting from underlying bodies of magma may persist in restricted geographical areas for tens of millions of years. Heirtzler et al. (1968) used magnetic reversals to date a series of submarine basalts in the North Pacific emitted from the same rift zone, the East Pacific Rise. The flows extend in age from the present (at the Pacific Plate-Juan da Fuca Plate boundary off Oregon and Washington) back at least to the oldest identifiable magnetic reversal at 80 X lo6 yr ago. A continental landmass of at least moderate relief is obviously needed close to such a tensional plate boundary to generate a sedimentary pile, if the high thermal gradient is to lead to significant overpressuring. The volcanism in the Taupo Volcanic Zone, New Zealand, is believed to have begun in the Upper Miocene, about 15 X lo6 yr ago, as dated by the marine beds in which redeposited pumice units are first seen. It has continued intermittently to the present day. Fossil hydrothermal mudflow conglomerates intercalated in a formation dated by pollen floras suggest that the associated geothermal activity at Wairakei is at least 5 X IO5 years old (Grindley, 1965). A fair number of the sedimentary sections with high heat flow are capped by shales (see locality descriptions in Ellis and Mahon, 1977). Thermal springs are evident and presumably account for much of the fluid flow, but if there are reasonable lateral permeability seals, a fluid-pressure differential adequate for driving some fluid upward across the shales may exist. If so, this component of flow would persist into the waning phase of a thermal event, until the fluid pressure differential bad become smaller than the sum of the hydrostatic and osmotic pressures (assuming salinity increasing downward). Lateral tectonic compression Overpressuring from lateral tectonic compression may also persist in restricted geographical areas for tens of millions of years. With this mechanism, the sediment pile typically results in part from tectonic thickening independent of the nature of concurrent sedimentation. Compressional plate boundaries are a locus of lateral compression at which magnetic-reversal dating may again be utilized. The most spectacular example of this sort is India, which has produced a total compression of the order of 1000 km in the 40 X IO6 yr since the end of the Eocene, when its northward movement brought it into contact with Eurasia (LePichon, 1968; Heirtzler et al., 1968). The Farallon plate and its apparent remainder, the Juan da Fuca plate, appear to have been underthrusting the North American plate and thereby exerting a compressive component against major portions of the U.S. West Coast for at least the last 50 X IO6 yr (Atwater, 1970). Even along the strike-slip San Andreas fault, which to the south of San Francisco has replaced the earlier trench, there is a compressive component until the Salton Sea and the widening Gulf of California are reached.

OSMOSIS

1439

If overpressuring results from the pore-volume decrease associated with a discrete lateral tectonic compression event, successive additional reductions of pore volume will be required to maintain overpressuring. There is an analogous requirement for all other mechanical means of generating overpressuring, e.g., in the next section of the paper, continuing sedimentation is required. Rapid deposition of fine-grained

materials

The development of pore pressure in excess of hydrostatic is assured if the deposition rate of clay-rich sediments exceeds a particular value, which depends upon sediment pcrmeability and the total thickness laid down by continuous sedimentation (Gibson, 1958; Skempton, 1970; Bredehoeft and Hanshaw, 1968; Sharp and Domenico, 1976). This condition is easily fulfilled in present-day deltas such as those of the Mississippi and Orinoco Rivers. On the other hand, compaction in regions of low sedimentation rate cannot generate overpressuring, which is consistent with the failure of Sayles and Manheim (1975) in pore-water studies of the Deep Sea Drilling Program to find evidence of semipermeable membrane behavior. The significance of this mechanism of overpressuring can be assessed by looking at the extent of the deltas of which the pertinent clay-rich units are part. The considerable worldwide extent of present-day deltaic sedimentation may be seen in Stoddart’s (1969) map of the magnitude of the solid load being deposited by various rivers. Thick sections of deltaic sediments occur in almost every geologic period from Precambrian on, and the deltaic depositional environment always occurs in various authors’ lists of those relatively few environments in which the vast majority of sedimentary rocks are deposited (Pettijohn, 1957; Blatt et al.. 1980). Bredehoeft and Hanshaw (1968) concluded from model calculations that fluid pressures approaching lithostatic can be produced with a continuing sedimentation rate of 500 m/lo6 yrs (reasonable for the Gulf Coast) to form a sediment column with a hydraulic conductivity of 1Om8cm/set (middle of the observed range of shales) or less. Further calculations by Sharp and Domenico (1976) assumed that overpressuring was driven by sediment compaction and were successful in reproducing present-day Gulf Coast distributions of temperature, porosity, and fluid pressure. These authors concluded that sediments in the Gulf of Mexico geosyncline have been overpressured since Late Cretaceous time (about 80 X IO6 yr, Kulp, 1961). Although Plumley (1980) argued that shale porosities in U.S.A Gulf Coast overpressured zones are too low to have resulted solely from nonequilibrium compaction of rapidly sedimented clays, there are probably supplementary contributions from mineral dehydration and aquathermal pressuring, so that an assumption of geologically long-lived overpressuring could still be valid. Geothermal gradients in normally-pressured sedimentary sections are low because of heat carried upward by fluid flow. It has been stated (C. E. Hottman, pers. comm. in Jones, 1969b) that the imposition of shale barriers in the U.S.A. Gulf Coast results in sharp increases in geothermal gradients across such shales, but there appears to be no good source of published data. Because of the finite permeability of capping shales, overpressuring from rapid deposition of fine-grained sediments will be dissipated at increasingly rapid rates if (a) the sedimentation rate decreases below a value critical for the particular depositional site, (b) sedimentation ceases, and (c) the area is uplifted and eroded. Mineral dehydration The dehydration of gypsum takes place in nature at a maximum depth of about 1 km (Graf and Anderson, 198 I),

1440

D. t. GRAF

too shallaw to be involved in most of the overpressured zones found in sedimentary piles @eju, 1973; Fertl, 1976). The model studies of Hanshaw and Bredehbeft (1968) indicated that the pulse of water retcased from an isolated source bed at depth will not generate an overpressured zone for a geologically significant time interval unless the water is retained behind a low-~~eab~lity bed. Even then, water released from a 15-m (SO-ft) thick gypsum bed at lithostatic pressure would move through shale with a hydraulic canduct&&y of lo-‘* cm”/sec to the overlying hydrostatic porefluid pressure region in the comparatively short time of 45 X 10’ yr. Maintaining overpressuring during continuing sedimentation by pulses of water released by successive gypsum beds at properly spaced intervals supposes a very uncommon stratigraphic succession. Smectite is often mixed with considerable amounts of other minerals, which means that post-dehydration compaction to force the released fluid into the pore volume of the rest of the section can at best be only partly effective. Canversion to a mixed-layered structure that still contains 20% smeetite iayers takes place on the U.S.A. Gulf Coast over a range of about 1.5 km (4900 ft) in depth, corresponding in time to about 3 X 10” yr (Hower or al., 1976). Dissipation of the fluid-pressure increment from smectite dehydration, by &rid flow across surrounding low-permeability beds, will operate throughout this long time interval, Hanshaw and Bredehoeft ( 1968) concluded that water loss from smectite may cause overpressuring if the concentration of smectite in a particular layer is very high and if the conductivity of the immediate stratigraphic section is low. It appears therefore that, in regions of normal thermal gradient, the release of water from smectite should make a slight to moderate, continuing contribution to the total overpressuring observed. This opinion is in agreement with Magara’s (1975b) judgment that montmorillonite dehydration is less important for overpressuring than compaction di~quilibrium (the retention of a large enough amount of pore water within shales that it bears part of the weight of the overlying rock column). GAINS AND LOSSES OF DISSOLVED SOLIDS

Ion exchange

The shifts in relative cation composition of pore of exchange positions are quantitatively inadequate to derive the observed cation compositions of deep concentrated subsurface brines, altkough they appear to be the

fluids possible from a single unloading

dominant

process

involved

in forming

some less sa-

fine, near-surface pore-fluid compositions (e.g., Foster, 1950). They are obviously of na help in explaining changes in total salinity or relative anion composition. Lambert’s (1978) strong emphasis upon ion exchange for explailning the origin of Delaware Basin brines containing up to 395,000 mg/l dissolved solids apparently involves a broad use of the term that includes chemical reactions involving more than the mineral surface. Control of @id compositfon by the diagenettic mineral assemblage Studies in Saline County, Missouri (Carpenter and Miller, 1969) and at Kettleman North Dome, California (Merino, 1975) have led to the conclusion that these subsurface brines, containing up to 30,000 ppm dissolved solids, are in thermodynamic equilibrium with the diagenetic min-

era1 assemblage. Merino’s demonstration that strings of plotted brine compositions have the slope and position to coincide with field boundaries on log activity/log activity plots is impressive. But subsurface brines range all the way up to 500,000 mg/l in dissolved-solids content, without any indication of discontinuity in frequency of occurrence (data of A. G. Collins cited in Carpenter, 1978). The difficulties involved in describing speeiation in these highly concentrated solutions were pointed out by Truesdell and Jones (1969), among others, and it is necessary to compute individual-ion activity coefficients in order to plot individual water compositions on lag activity/log activity diagrams. The various models that treat individual ions, utilizing extended DebyeHuckel coefficients and allowing for ion pairs (Gariels and Thompson, 1962; Helgeson, 1968a; Helgeson et al., i 969b3; Truesdell and Jones, 1969; Helges~n et af., 1970; Kharaka and Barnes, 1973; Truesdell and Jones, 1974; Plummer er al., 1976; Ball et a!., 19791, are most appropriate to difute solutions, as noted by Harvie and Weare (1980). Another group of models yields stoichiometric mean activity e&IIcients, from which solubilities can be cakufated in order to define phase fields and monitor precipitation from waters that become supersaturated. The secund-virialcoefficient models of Lerman ,(1967) and Wood (1975, 1976) are moderately successful for concentrated solutions, but the model of Harvie and Weare (1980) that incorporates higher-order virial coefficients appears to be required to treat systems in which NaCl is not dominant and to obtain accurate results over the full concentration range. The subsurface brine system Na-K-Mg-Ca-Cl-Hz0 is a subsystem of the system treated .by Hervie and Weare (1980) at 25°C. Recomputation of phase diagrams relating diagenetic mineralogy and brine composition,- using this model, would require knowledge of the subsystem at several moderately elevated temperatures, which in turn would require isopiestie data for the appropriate compositions at the several temperatures. Some modification of existing phase diagrams might be anticipated. A more fundamental point is that many of the stability fields on such diagrams (e.g., see Helgeson et al., 1969a) extend over several orders of magnitude in activity, a much larger effect than the expectable changes from chemical osmosis. If salt filtration merelv alters the concentration of the brine but does not supersaturate it, the brine will retain this compositional information except for possible subsequent ion exchange reactions. If su~rsaturation occurs, the commonest result will be the meciuitation of additional amounts of one or more of the equifibrium diagenetic solids. This event is likely to be diflicuIt to reconstruct later, either because the volume of precipitate is very small or precipitates onto existing grams in optical continuity, or because of the difficulty of distinguishing and dating precipitates of several ages. Brine-solid equilibrium does not preclude the concurrent operation of shale membranes, and the brinehistory osmotic models that have considered concentrations of individual ians (e.g., Graf ef al., 1965; 3erry, 1947; Hitchan et al., 1971) have typically been hybrids that also invoked selected chemical reactions. The assumption of thermodynamic equilibrium between brine and late diagenetic minerals implies not only that such systems will be able to adjust if membrane concentrates are added to them, but that the considerably different mineral assemblages (stable or metastable) that existed during early sediment diagenesis have been reconstituted. Merino (1975) considered that glauconite, phosphatic pell gets, pyrite, and probably some kaolin&e had failed to react at the --1tW’C in situ temperature at Ketfieman North Dome, and are not now in equilibrium with the interstitial brine, A brine temperature range of 2%2509C incfudes. many of the temperatures that various authors- have believed necessary if particular sedimentary reaction5 are to behave reversibly. Thus, Eltis and Mahan f 1977) concluded

CHEMICAL that equilibrium concepts can only be used with confidence above about 175°C. Carbonates and silicates reached oxygen isotopic equilibrium down to 150°C and possibly down to 100°C in the Salton Sea geothermal field, California, but detrital quartz was still resistant to isotopic exchange at 340°C (Clayton et al., 1968). Sulfate

loss

The decreasing solubility of Ca sulfate minerals with depth of burial has been invoked as a means of decreasing the SOi- concentration in solution (Ellis and Mahon, 1977). Anhydrite is the mineral of greater interest because, in regions of normal geothermal gradient, gypsum converts to it at depths from 0.61 to 1.07 km (2000 to 3500 ft) (MacDonald, 1953; Stewart, 1963; Murray, 1964; Graf and Anderson, 1981). The (metastable) solubility of anhydrite in water at 25°C and 0.101 MPa (1 atm) is about 0.028 molal, which drops to about 0.0015 in water at 150°C and the vapor pressure of water, or to about 0.0029 in water at 150°C and 50 MPa (500 bars) total pressure, and rises to about 0.020 molal in a 4 molal NaCl solution at 150°C and 0.1 MPa (1 bar) total pressure (Blount and Dickson, 1973). The claimed solubility decrease is therefore valid for low-salinity geothermal waters in volcanic terrains, much less so for concentrated NaCl brines in sedimentary sections. However, if the latter are also rich in CaCl*, there will be an additional decrease in anhydrite solubility because of the Ca*+ common-ion effect (Locwengart, 1962). Pore waters out of contact with the atmosphere that encounter Fe2+, Mn in reduced states, and organic matter lose their oxidizing ability. These fluids at depth and elevated temperature are likely to be moderately acidic (Ellis and Mahon, 1977) so that the equilibrium between S2- and SOi- would strongly favor the former (Garrels and Christ, 1965, p. 2 14). This ionic reaction is kinetically hindered in the lower-temperature portion of the diagenetic range, but it is aided there by the intervention of SOi--reducing bacteria. The total amount of diagenetic and low-grade metamorphic pyrite formed is a clue to the effectiveness of this SO:-- -removal mechanism. There is about 2.5% wt % pyrite in the central portion of the Salton Sea geothermal area (Helgeson, 1968b), where the pore fluids are of nonmarine origin but sulfate-rich. Pyrite is very common in black shales of chlorite and biotite grade in regional metamorphism. Loss of CO2 species There are at present a few CO,-rich hot springs in the Salton Sea geothermal area (Helgeson, 1968b), and CO* is concentrated in permeable sands at lOO- to 200-m (328to 656-ft) depth (Muffler and White, 1969; Ellis and Mahon, 1977). The gas contained in steam from wells and fumaroles at Wairakei is mostly CO* (Ellis and Mahon, 1977, p. 350). The CO2 released at depth by reaction of carbonates to form metamorphic silicates does indeed appear to be more mobile than the dissolved ions of the pore fluids. By escaping so far up the stratigraphic column, it limits the amount of Ca *+ that might be brought into the pore fluid at intermediate depths by dissolution of carbonates. The escape of CO* is facilitated by the way in which its solubility in pore-fluid varies with temperature and salinity (Ellis and Golding, 1963). It becomes less soluble in pure water up to about 160°C. but increases again above that temperature. However, it decreases in solubility with increasing concentration of dissolved salts, an effect that in the Salton Sea brines would more than compensate for the temperature effect above 160°C. If the concentration of Ca2+ in solution is increased by processes not involving gain or loss of CO*, such as dolomitization of limestone and membrane cation selectivity in

1441

OSMOSIS

osmosis, the solubility product of CaCO, may be exceeded and the resulting CaCO, precipitation will diminish the total of dissolved CO2 species, as noted by van Everdingen (1968). Additional

calcium

sources

Calcic plagioclase breaks down to albite and other reaction products at temperatures as low as 160°C and depths as slight as 61 m (200 feet) at Steamboat Springs, Nevada (Schoen and White, 1965) but it persists metastably to 360°C in contact with the concentrated, Ca2+-rich brine of the Salton Sea area (Muffler and White, 1969). This potential increment of Ca*+ to solution can also be lost in environments of low aco2/aH20 ratio by the precipitation of laumontite or other zeolites (Zen, 1961; Merino, 1975). The solubility of CaCOS decreases rapidly with increasing temperature, but increases with increases of hydrostatic pressure, pcoz, or non-Ca-containing dissolved salts (Holland, 1967; Ellis and Mahon, 1977, pp. 137-141). It decreases because of the common-ion effect if Ca2+ from another source is added to solution, or if a pH controlled by other equilibria is increased (because the CO:-- ions become a larger fraction of a fixed total-carbonate-species population). These equilibria are used by Ellis and Mahon (1977) to explain a number of interesting features of water chemistry in low-salinity geothermal areas, but they do not permit the development of concentrated CaCI, brines to be furthered by simple dissolution of CaCO,. Sources

of magnesium

Discussions about the MgZf in subsurface brines are typically concerned with reactions that remove it from solution. Perhaps of even greater interest is the source in those cases where there is enough Mg2+ so that it persists as a major brine cation in spite of losses to diagenetic mineral formation The Mg*+ content of low-salinity, somewhat acid geothermal waters in New Zealand, Iceland, and Japan is very low, commonly 0.001-0.1 ppm (Ellis and Mahon, 1977). The alteration of FeMg minerals of volcanic rocks to chlorite in these areas apparently proceeds efficiently without Mg2+ buildup in solution. The Mg2+ concentration was found to be 1 ppm or less for CO,-charged water in contact with magnesian chlorite + calcite + quartz in experiments by Ellis (1971) at temperatures from 190” to 300°C. The very low Mg*+ content of the concentrated chloride brines of the Salton Sea geothermal area (Helgeson, 1968b) has already been mentioned. What the above occurrences have in common is the virtual absence of marine sediments and marine pore fluids. The brines at depth in typical basins with thick marine sections are more Mg’+-rich principally because there is a major additional Mg’+ source. If there are evaporites in the basin, then pore fluids may have been enriched by K+- and Mg2+-rich residual liquids from that facies. If there are not, then normal sea water has to be the Mg*+ source, as postulated by several of the existing membrane-filtration models. Temperatures are somewhat lower in these basins than at comparable depths in geothermal areas, slowing the rate of chlorite formation, but on the other hand there is typically more limestone available for dolomitization, so that an alternate explanation based upon reaction rate seems inadequate by itself. Chloride

sources

In apparently evaporite-free basins such as the Illinois Basin, where pore-fluid chlorinity can be assumed not to have been altered by precipitation or dissolution of halite and other chloride minerals, there are two possible ways to obtain the large amount of Cl- needed for concentrated

D. L. GRAF

1442

brine. One is to retain and concentrate the dissolved-solids content of marine pore fluid, and the other, closely related, is to leach and concentrate dissemiaatcd Cl- within mineral structures and on grain surfaces (Berry, 1967). It might he possible, in exceptional cases, to Ieach as much as several thousand ppm Cl- from the volcanic rocks in a geothermal area (Ellis and Mahon, 1977). Johns and Huang (1967) estimated the average Cl- content of igneous rocks to be 185 ppm, of sedimentary rocks, 105 ppm, so that leaching of non-evaporite sedimentary rocks must play at best a subordinate role in Cl- accumulation.

DISCUSSION AND CONCLUSiONS Overpressuring generates adequate fluid-pressure differentials to drive reverse chemical osmosis. Taken together, the overpressurings from three of the most important mechanisms, rapid sedimentation of finegrained materials, tectonic compression, and abnormally high thermal gradients, is effective at any given time in portions of many of the existing sedimentary basins. Overpressuring driven by a single geologic event may persist in a given area for a million to several tens of millions of years. Although basin-wide ~rrelations through time between shale dist~bution and fluid flow patterns have not yet been attempted, the D/H studies of Clayton et al. ( 1966) and Hitchon and Friedman (1969) indicate that most sedimentary basins contain enough shales so that considerable micropore flow takes place at one or more intervals during basin history. Laboratory studies, in turn, demonstrate that micropore flow will make nontrivial contributions toward increased salinity and altered ion ratios, even if the input fluid is several times as concentrated as sea water. Reverse chemical osmosis must therefore be at least a subordinate process in generating the pore-fluid compositions observed in sedimentary rocks, leaking fluid of low solute content from overpressured regions. It aperates in this sense today on the U.S.A. Gulf Coast, for example. Even though shale permeability is low, the large area of formational interface and the substantial time interval involved cooperate to produce a sizeable volume transfer. The more difficult question is the relative importance in a particular region of the several processes contributing toward the solute content behind the shale barrier. If the stratigraphic section there is devoid or essentially devoid of evaporites, then the membrane filtration of dissolved constituents in marine-derived pore fluid becomes very important as a source of Mg*+ and Cl-, in particular. The aiternatives of invoking eroded evaporites, undiscovered evaporites, or the tectonic injection of evaporite brines from an adjoining basin are not obviously more plausible. The mechanism of overpressuring will differ from region to region. If rapid sedimentation were the only means of producing it, overpressuring would always disappear after uplift. All Paleozoic and older basins would be like the Iilinois Basin, normally pressured even though there are a good many shales in the

section, but retaining chemical and stable isotopic hints of an earlier period of overpressuring and salt filtering. So the present-day occurrence of overpressuring in rocks all the way back to Cambrian (Deju, 1973; Fertl, 1976) requires additional mechanisms that can be imposed later in the history of a basin. Typically, several mechanisms may be involved in a particular region, e.g., possible contributions from rapid sedimentation, tectonic compression, mineral dehydration, and aquathermal pressuring because of thick shale insulators in the Central Valley of California. Plumley (1980) concluded that shale porosities in U.S.A. Gulf Coast overpressured zones are too low to have resulted solely from rapid sedimentation, and that mineral dehydration and/or aquathermal pressuring must also have been operative. The interpretations made in an earlier section from pressure calculations are overly pessimistic in two respects. The first point to be made is that the regular downward increase in salinity utilized by the model is not that observed for sections containing overpressured segments, for the pore fluids of those segments are often markedly low in salinity (and high in porosity) for their depth. The explanation appears to be that compaction has not taken place to the extent that it has in adjacent normally-pressured segments, so that there has been less op~rtunity for low-salinity membrane efl’luent to escape and thereby to leave behind a residue of enhanced salinity. If salinity does increase with depth through an overpressured segment, but at a reduced rate, the osmotic pressures to be overcome will be reduced below those calculated above and the enhanced net upward fluid pressure will drive salt filtration at a faster rate. If the pore fluid of the overpressured zone is actually less saline than that at the bottom of the overlying normally-pressured zone, as described by Kharaka et al. (1977) for the Corpus Christi area, osmotic pressure and overpressuring will cooperate in increasing the salinity of the overpressured zone at an even faster rate. The second point is that there are some conditions under which the relatively modest fluid pressure contribution from the topographic position of recharge areas can be effective. In a normally-pressured section with salinity increasing steadily downward as in the model, water will move upward across a shale separating two aquifers if the value of (difference in elevation of recharge areas for the aquifers)/(difference in elevation of aquifers in basin) is enough greater than the average value of this ratio for the whole sedimentary section. Further, if the downward salinity increase is enough lower than the model average, or even reversed, then a merely average difference in elevation of recharge areas for two aquifers will drive upward tlow. However, the small effect from topography obviously cannot be added onto a larger overpressuring generated within a shale seal by other mechanisms, because estabIishing hydraulic continuity through an aquifer to the surface would

CHEMICAL

only initiate fluid movement back up the aquifer and reduce the existing overpressuring. The topographic contribution to fluid pressure should most often be of importance for salt filtration in low-salinity, relatively near-surface environments. Pore diameters are larger in clay-rich rocks there than at depth, but a thicker double-layer is required in the less saline solution to balance surface charge, so that the entire pore cross section may still remain charged. There is, of course, an upper limit to effective pore diameter; osmotic processes were of minor im~rtance in experiments conducted by Bresier (1972) and Bresler and Laufer (1974) with slurries having high water/clay ratios. It follows that the replacement in Illinois Basin pore fluid of water molecules from the ocean by those of local meteoric precipitation (Clayton et al., 1966) probably took place after decay of overpressuring. This interior region was essentially free during the post-Precambrian of tectonic and thermal events, so that the mechanism principally responsible for the overpressuring was probably depositional. The freshwater hydrostatic heads stemming from the modest topographic relief of the area would have been particularly low and unable to prevail against even slight depositional overpressuring. However, the exchange of water within a particular bed presumably took place before later marine invasions had deposited a sufficient thickness of overlying beds that fluid flow in this bed was greatly slowed. There is an analogy to bacterial sulfate reduction, which is most effective in a zone at the top of a growing marine sediment pile because of lower temperature and more abundant organic matter. A general observation about demonstrating the operation of osmosis or reverse osmosis at a particular locality is that if only a single membrane process is claimed, there will often be more conventional geologic processes that could have produced the observed effect. Discrimination among the possibilities frequently involves detailed arguments about geologic history. A more convincing demonstration would be possible if concurrent membrane transport because of temperature and electrical-potential gradients were also involved. The variations within a stratigraphically restricted zone of several properties, e.g., fluid pressure, self-potential, Na’/Ca*+ ratio and temperature would have the proper magnitude ratios with respect to each other to have resulted from the effects of a shale membrane superposed on regionai values of these properties. Because of the difficulty of making the several kinds of quantitative measurements involved, this test appears never to have been carried out. The contamination of boreholes with drilling mud and the considerable time required for thermal reequilibration are well understood, and corrections may be made (Kharaka et al., 1977) for the dilution of formationwater samples from gas wells by water vapor that was produced with natural gas and then condensed.

I443

OSMOSIS

But there is no way to correct for the effects of waste brine reinjection and pressure drop from production, so that there may be only a limited number of years during the development of an oil or gas field when there are enough holes for adequate geochemical sampling, but the original parameter distributions are still unaltered. paper has benefitted substantially from the comments of M. E. Bickford, P. A. Domenico, B. B. Hanshaw, A. T. Hsui, Jon Holder, John Hower, B. F. Jones, Y. K. Kharaka, H. W. Olson, and several Acknowledgments-This

reviewers who took their job seriously. It is a byproduct of an experimental program supported over some years by grants from the U.S. Army Research Office and the Earth Sciences Division, National Science Foundation. Permission of the Illinois State Geological Survey to reproduce Fig. 3 of Graf er nl. (1966) is gratefully acknowledged. Laura Harbison and Carol Sanderson typed the successive revisions of the manuscript with skill and patience. The Geochemicai Society sponsored the session on “Shales and Subsurface Hydrology” at the annual meeting of the Geological Society of America and affiliated societies in Cincinnati, Ohio, in November, 1981, at which part of this material was presented.

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port in thick sequences of compacting sediment. Geof. Sot. Amer. Bull. 87, 390-400. Sifvester L. F. and Pitter K. S. fl977) Therm~ynamics of electrolytes. 8, high-tem~rature properties, including enthalpy and heat capacity, with appiication to sodium chloride. J. Phys. Chem. 81, 1822-1826. Skempton A. W. (1970) The consolidation of clays by gravitational compaction. Quart. J. Geol. Sot. London X25, 373-411. Skinner B. J, (1966) Thermal expansion. In ~u~~ok of Pkysicul Co~t~ts (ed. S. P. Clark), Gpol. See. Amer. &fern. 97,75-96. Sorensen H. 0. and Segall R. T. (1974) Natural brines of the Detroit River Group, Michigan Basin, In Fourth Symposiumon Salt (ed. A. H. Coogan) 1,91-99. Northern Ohio Geol. Sot. (Clevetand). Stevenson D. L., Chamberlin T. C. and Buschbach T. C. (1975) fnsolubfc residues of the Sank sequence (Cambrian and Lower Ordovician) rocks of the Fair&Id Basin, Illinois: an aid in correlation and in petroleum exploration, Illinois Geoi. Surv., Iilinois Petrol. 186, 12 pp. Stewart F. H. (19631 Marine evanorites. U.S. Geol. Sun: P?t$ Paper &O-u, 52 pp. Stoddart D. R. (1969) World erosion and sedimentation, In Water, Earth, and Man fed. R. J. Chorley), pp. d36 1. Methuen. T&h J. (1979) Patterns of dynamic pressure increment of formation-~uid flaw in large drainage basins, exempl~~ by the Red Earth Region, Alberta, Canada. Bull. Con. Petrol. Geol. 27,63-83. T&h J. (1980) Cross-formational gravity flow of groundwater: a mechanism of the transport and accumulation of petroleum (the generalize& hydraulic theory of petroleum migration). In Problems of Petroleum ~igrution (ed. W. H. Roberts HI and R. J. Cord&l), Amer. Assoc. Petrol. Geol., Studies in Geol. 10, 121-167. Truesdell A. H. and Jones B. F. (1969) Ion association in natural brines. Chem. Geol. Q 51-62. Truesdell A. H. and Jones B. F. f 1974) WATEQ, a computer program for calculating chemical equilibria of natural waters. J. Res. U.S. Genl. Surv. 2, 233-248. van Olphen H. (1977) An Introduction to Clay Colloid Chemistry, 2nd ed., 318 pp. Wiley. van Engelhardt W. and Gaida K. H. (1963) Concentration changes of pore solutions during the compaction of clayey sediments. 3. Sed. Petrol. 33,9 19-930.. van Everdinzen R. 0. ( 19681 Mobilitv af main ion snecies in rever~osmosis and the modification of subsurface brines. Can. J. Earth Sci. 5, I ET?-1260. Wardlaw N. C. (1972) Unusuai marine evaporites with salts of calcium and magnesium chloride in Cretaceous basins of Sergipe, Brazil. Econ. Geol. 67, 156168. White D. E. (1965) Saline waters of ~i~ntary rocks. In Fluids in Subsurface Envitwnments (ed. A. Young and J. E. Galley), pp. 343-366. Amer. Assoc, Petrol Geol-

ogim. White D. E. (1968) Environments of generation of some base-metal ore deposits. &on. Goof. 63. 301-335. White D. E., Hem J.*D, and Waring G. A. (1963) Chemical composition of subsurface waters. Li.S. Geol. Surv. Prof. Paper 44OF, 67 pp* Wood J. R. (1975) Thermodynamics of brine-salt equilibria-L The systems NaCl-K~l-MgCl~-~a~l~-H~~ and Na~i*Mg~~-~~~ at 25*C. Geochim. Cosrn~h~m Acta 39, 1147-1163. Wood J. R. f 1976) Therm~namics of brine-salt equifibria-II. The system NaCl-KCI-H,G from 0 to 200% Geochim. Cosmochim. Acta 40, 12 1 1- 1220. Zak I. t 19801 The acjochemical evolution of the Read Sea. In Fifih Sympo&m on Suit (ed. A. H. Coogan and L. Ha&et) 1, 181-l 84. Northern Ohio Geol. Sot. (Clevcland). Zen E. (1961) The zeolite facies: an interpretation. Amer. J. Sei. 259.401-409.

CHEMICAL APPENDIX

1447

OSMOSIS

I

SOME THERMODYNAMIC RELATIONS Suppose a rigid box (Fig. 6) to be separated into two compartments by a rigid membrane permeable to water molecules but not to Na+ and Cl- ions. If side I is filled with pure water, and II by NaCl solution, both at 0.101 MPa (1 atm) pressure (P’ = P” = P,), ahs will be greater will flow from I into II until aXfl than a&o. Water = a& at which point PI’ will have increased to PO+,+The increase in aRfl results from two effects, the increase in the water molecule to ion ratio in the solution and the increase in pressure. The osmotic pressure ?r is that pressure that would have to be applied to II initially (replace the bottom of the box with a movable piston) to prevent any flow of water from I to II. It is equivalent to the sum of the two activity increments, and is therefore even larger, K = PO+*+<. The shales that are the principal semipermeable sedimentary membranes have pore walls with a net negative charge because of the substitution of lower-charge cations for framework Al’+ and Si4+ in clay minerals. If the pores are small enough in diameter so that the charge on their walls is felt throughout the pore cross section, Cl- ions will suffer electrical repulsion and be unable to pass through the pore. Na+ ions will form an electrical double layer within the pore that partially balances the negative charge, and will be able to pass through the pore, but in the absence of balancing Cl- ions they will accumulate at the pore exit and quickly build up a potential gradient along the pore that stops further cation flow. In nature, chemical osmosis produces an over-pressuring on the high-salinily side of the shale, i.e., a fluid pressure greater than that which would exist if the fluid column with its defined temperature and salinity distributions had an uninterrupted connection to the surface through macro-channels. If P” in Fig. 1 is further increased to P,,+b+c+drwater will flow from the more saline to the less saline side of the membrane. Physical chemists noted that this flow is the reverse of what one would expect from an initial consideration of the membrane at 0.101 MPa (1 atm) pressure. Shales are in general less than 100% efficient in holding back ions, and in a complex solution will have greater efficiency for some ions than others. Efficiency increases with increased cation exchange capacity of the clay mineral, with increased compaction pressure, with decrease in salinity of input solution, and (slightly) with decreasing temperature (Kharaka and Berry, 1973). In nature, the operation of reverse chemical osmosis requires that some non-osmotic process generate an overpressuring on the high-salinity side of a shale that is greater than the overpressuring produced by chemical osmosis. The chemical osmotic pressure difference between a more saline NaCl solution II and a less saline I solution is P” - P’ = RT(ln

a: - In atf)/F,

where a, is the activity of water, T is temperature in degrees Kelvin, R is the gas constant (83.15 cm’ MPa deg-’ mole-‘), and I’, is the molar volume of water (Guggenheim, 1959, p. 235; Hanshaw and Zen, 1965). The activity of water can be obtained from a, = exp( - Mw4NacIvNaCImNaCIl 1000) = exp(-0.0360304NaCImNaCI

),

where M is molecular weight, u is the number of charged particles into which a formula of the solute dissociates, 4 is osmotic coefficient, and m is molality (Rush and Robinson, 1968). The standard state for the solvent at each depth is pure water at the same temperature and fluid pressure as the brine at that depth, so that if the less saline solution I be taken in each calculation as pure water, In at, goes to zero. The choice is apt for this problem, because the chem-

pl,aIHO 2

p4a;, 9

2

m NaCl FIG. 6. Two-compartment, rigid-box model to describe pressure and concentration effects produced by a rigid membrane permeable to H,O but not to Nat or Cl-. ical contribution to pressure is clearly identified. The quantities 4N.c, and V, describe the total osmotic system, the two sides of which may be at substantially different pressure, yet both of these parameters are pressure dependent. Because the dependence is weak, evaluating them at (P’ + P”)/Z suffices. Kennedy and Holser ( 1966) tabulated values of the specific volume of water as a function of temperature and pressure (in bars). Values of 4N.CI as a function of temperature and salinity were computed by Pitzer et al. (1979) using the same standard state convention as mentioned above (see Silvester and Pitzer, 1977). The initial portion of their equation is 4 -

1 = -Iw,lAm

(P”)

(l+

+ ...

where b is a constant, A, is the Debye-Htickel coefficient for the osmotic function, zs, is the signed valence of the cation, zx is that of the anion, and I is ionic strength, I = r/2 C m,zf The first term on the right arises from long-range electrostatic interactions, and succeeding terms treat short-range M-X interactions and indirect forces arising from the solvent. The portion of the temperature dependence of 4 - 1 that arises from the first term drops from about 100% at 1.2 m NaCl to about 25% at 5.7 m NaCl. Bradley and Pitzer (1979) have calculated A, as a function of both temperature and pressure, and over the range of conditions of our model the pressure dependence of A, is only about an eighth the temperature dependence. The values of 4N.C, used in this paper have been modified to include the pressure-corrected A, term, a correction that is in the right direction and is the best that can be done until tables of 4NaCI as a function of pressure appear. This correction decreases calculated osmotic pressures by a maximum of 3%.

APPENDIX Ii SAMPLE CALCULATIONS The tables of Phillips et al. (1981) give NaCl solution density (g/cm’) as a function of pressure (bars), temperature (“C), and molality of NaCI. The calculations of this paper, concerned with estimating relative sizes of fluid-pressure contributions, involve only linear interpolation and extrapolation and arithmetic iteration. If the sediment-water system were to be followed through time with an appropriate set of differential equations, the discussion would have to be focused on a restricted geographical region whose geologic history is well understood. Hydrostatic pressure At 1250-ft (0.38 1-km) depth, the midpoint of the topmost 0.762-km block of the model section, the temperature is

144X

I>. I.. GRAF

23.4”C (12°C at surface, 3O”C/km) and the pore fluid is 0.3 molal in NaCl (17,530 g NaCl/106 g H,O). At saturation vapor pressure (Phillips ei al., 1981), the solution density interpolated over concentration and temperature is 1.011072 g/cm’. The hydrostatic pressure is (0.381 km)(l.O11072 g/cm3)(l@’ cm/km)(lO-s kg/g) - 38.5218 kg/cm’or 38.5218 (0.980665) = 37.7770 hars. Interpolate in Phillips et al. (1981) over concentration, temperature. and pressure to get a density of 1.017541 at 37.7770 bars. Recalculate hydrostatic pressure using this new density, and continue this iteration until a solution density of 1.017583 g/cm3 at a tabulated pressure of 38.0203 bars yields the same value in bars for the hydrostatic pressure at 0.38 I km depth. The hydrostatic pressure at 3750-ft (1.143-km) depth after iteration is 2(38.0203) + 38. I( 1.029359)(0.980665) = 114.5003 bars, where 1.029359 g/cm3 is thedensity at 114.5003 bars. Hydrostatic pressure increase with temperature; pore volume, NaCI molality, and solution density constant At 21,250-ft (6.477-km) depth, the midpoint of the next to deepest 0.762-km block of the model section, the temperature is 154.5”C (12°C at surface, 22”C/km), the pore fluid is 5.1 molal in NaCl, the computed hydrostatic pressure is 672.28 bars, and the solution density is 1.096014 g/ cm3, If the thermal gradient below 10,000 ft (3.048 km) is raised to 30”C/km, the temperature at 21,250-ft (6.477. km) depth becomes 182.O”C. Interpolate over temperature and density in Phillips er a/. (1981) to find the NaCl molalities at (700 bars, 182.O”C 1.096014 g/cmj) and (1000 bars, 182.O”C, 1.096014 g/ cm’). Interpolate between these two molalities to find that m = 5.1 corresponds to a pressure of 975.89 bars, an increase in hydrostatic pressure of 303.61 bars. Hydrostatic pressure decrease with thermal expansion aj enclosing rock; temperature and NaCl molality constant Refer to the immediately preceding calculation. The thermal expansion of a volume-weighted mineralogical-average sedimentary rock (see text) on going from 154.5”C to

182.O”C is 0.089%. If the pores increase m voiume by the same percent, then the resulting solution density is i .0960 14/ 1.00089 = 1.095039 g/cmj. Interpolate over NaCI molality . temperature, and density in Phillips er al. ( 198 I ) to find that (154.5”C, 5.1 molal, 1.095039 g/cm3) corresponds 1~1 a fluid pressure of 653.78 bars, a decrease of I X.50harr Percentage mass (volume) lass jrom ,fluid rescfwtr t(i reduce fluid pressure from lithostatic ta h,~~drastatit:~ rock framework remains rigid. no salt filtration during loss Continue with the first example of thts hppendtx, whtch was at 1250-ft (0.381&m) depth. Specific volume of pore fluid at hydrostatic pressure = 1/I .017583 = 0.98272 I cm’! g. Interpolate in Phillips et al. (1981) over pressure, temperature and NaCl molality to get density of pore fluid at I .025708 lithostatic nressure (85.47 bars. 23.4”C. 0.3 m) g/cm’, anda specific volume = 0.974936 cm’jg. Percentage volume (mass) loss = iOO(O.982721 11.974936): 0.974936 = 0.80. Percentage mass loss from fluid reservoir to redwe jiuid pressure from lithostatic to hydrostatic: rack fiatnewark remains rigid, salt jiltration during loss is IOO% efficient Relative to the immediately preceding example, the bydrostatic pressure attained now will be that for an enhanced vertical salinity gradient, and the pure water that escapes will be a lesser mass percentage of the fluid reservoir. For example, at 5.7 15-km (18,750-ft) depth, read 4. IS’6 from curve “a” of Fig. 5 for the preceding case. Then, Ignoring the slight hydrostatic pressure increase from the increase in fluid density produced by salt filtration, use the brim density of 1.058208 obtained for 7’ = 183.5”C and hydrostatic pressure = 582.47 bars in the initial model hydrostatic pressure calculation. Interpolate from the tables of Kennedy and Holser (1966) a specific volume for pure water at this pressure and temperature of 1.0900, and take tts reciprocal. Then the percent of mass lost from the fluid reservoir in this second case is 4.15(0.9174/( 1.0582) -- X60