Reactive transport modeling of early burial dolomitization of carbonate platforms by geothermal...

AUTHORS

Fiona F. Whitaker � Department of EarthSciences, University of Bristol, Bristol BS8 1RJ,England, United Kingdom;[email protected]

Fiona Whitaker is a senior lecturer in Earth Sci-ences at Bristol University and leader of theBristol Carbonates Consortium. Her researchfocuses on carbonate sedimentology and dia-

Reactive transport modelingof early burial dolomitizationof carbonate platforms bygeothermal convectionFiona F. Whitaker and Yitian Xiao

genesis, integrating field studies of modern en-vironments with numerical modeling to providea holistic understanding of the evolution ofporosity-permeability in carbonate sediments.She has a B.Sc. degree in physical geographyand a Ph.D. from the University of Bristol, whereshe studied the hydrochemistry of modernBahamian carbonate platforms.

Yitian Xiao � ExxonMobil Upstream ResearchCompany, P.O. Box 2189, Houston, Texas 77027;[email protected]

Yitian Xiao is a senior geoscientist at ExxonMobilUpstream Research Company. He has exten-sive experience in applying reactive transportmodels to characterize carbonate and siliciclas-tic reservoirs for solving both geoscience andengineering problems. His current project in-volves the use of process-based models, includ-ing reservoir simulations to investigate uncon-ventional gas reservoirs (shale gas, coalbedmethane) as well as CO2 and sour gas injection.He also maintains a strong research interestin applying computational chemistry to modelsource rock maturation and oil and gas gen-eration. He has a B.S. degree in geochemistryfrom China and he received his M.Ph. degreeand his Ph.D. in geochemistry from Yale Uni-versity. He has been an adjunct faculty in theEarth Science Department at Rice Universitysince 2001 and currently serves as a dissertationadvisor for Ph.D. students at Indiana Universityand University of Bristol, United Kingdom.

ACKNOWLEDGEMENTS

ABSTRACT

Reactive transport models (RTMs) permit quantitative inves-tigation of diagenesis and its effects on reservoir quality. TheRTM TOUGHREACT is used to investigate diagenesis in anisolated platform driven by geothermal (Kohout) convectionof seawater, which has been invoked to explain dolomitiza-tion during early burial. Previous short (0.1 m.y.) RTM simu-lations suggested that convection can drive dolomitization,mostly at greater than 50°C, and anhydritization, but completedolomitization requires greater than 30–60m.y. Ourmore ex-tended RTM simulations (<30 m.y.) indicate significant non-linearities in the system, consistent with high-temperature ex-periments, with parts of the platform completely dolomitizedwithin 10–15m.y. As dolomitization proceeds, the process be-comes predominantly flux controlled, with development of awedge-shaped dolomite body, which thins from the margin tothe interior, at considerably shallower depth and cooler tem-peratures (20–30°C) than suggested by short simulations.Dolomitization is relatively insensitive to boundary conditionssuch as relative sea level and platform geometry but is signifi-cantly slower in circular than elongate platforms. Sedimentpermeability and reactive surface area, commonly inverselyrelated, are key controls. Dolomitization is limited to the mar-gin of low-permeability muddy platforms despite a high reac-tive surface area. Dolomitization of more permeable grainyplatforms is limited by a lower reactive surface area, occurringonly in the platform core due towidespread cooling. Sedimen-tary layering produces a complex diagenetic stratigraphy,

This article has benefited from discussions withmany colleagues, including Tianfu Xu, GarethJones, Peter Smart, Hans Machel, and RolfArvidson, and also from reviews by StephenKaczmarek, Stephen Ehrenberg, and MarkCopyright ©2010. The American Association of Petroleum Geologists. All rights reserved.

Manuscript received April 22, 2009; provisional acceptance July 20, 2009; revised manuscript receivedOctober 13, 2009; final acceptance December 9, 2009.DOI:10.1306/12090909075

AAPG Bulletin, v. 94, no. 6 (June 2010), pp. 889–917 889

Longman. FFW thanks ExxonMobil URC for sup-porting stimulating academic exchange visitsbetween URC and Bristol. The views expressedin this article by Yitian Xiao are his own and notnecessarily those of ExxonMobil.The AAPG Editor thanks the following reviewersfor their work on this article: Stephen N. Ehrenbergand Mark W. Longman.

DATASHARE 36

Two supplementary figures are accessible in anelectronic version on the AAPG Web site (www.aapg.org/datashare) as Datashare 36.

890 RTM of Geothermal Dolomitization

dolomitization favoring more reactive beds at shallow depthwhere permeability is not limiting, but switching to morepermeable beds at depth. Bank-marginal fracturing limits do-lomitization of the platform interior, whether the fractures arebaffles or conduits for flow.

INTRODUCTION

Some 50% of the world’s carbonate rocks are dolomitized(Zenger et al., 1980), and dolomite reservoirs contain signifi-cant volumes of the global hydrocarbon resources. Predictionof the spatial distribution of dolomitization and its effect onreservoir quality is thus of fundamental importance in reser-voir characterization. Dolomite can behave as a reservoir oras a baffle/barrier to flow depending on the original deposi-tional texture, style of dolomitization, and presence of anhy-drite cement (Cantrell et al., 2004; Ehrenberg, 2004). Thefrequency and nature of limestone-dolomite transitions thatdefine flow units and baffles or barriers are critical for under-standing reservoir connectivity and producibility, and opti-mizing field development (Cantrell et al., 2004; Xiao andJones, 2007). Existing subsurface dolomite predictions aremostly based on field observation and are occasionally linkedto sequence stratigraphy. This approach can be relatively suc-cessful at predicting general trends in limestone and dolomiteoccurrence, but considerable uncertainty in predicting andcorrelating spatial variations in diagenetic styles at the fieldscale exists (Xiao and Jones, 2007). In addition, dolomitiza-tion may be an important factor in the secular changes in sea-water chemistry through the Phanerozoic (Holland, 2005) andmay contribute to the formation of Ca-enriched, Mg-depletedbasinal brines (Hanor, 1988).

Most dolomites (CaMg[CO3]2) are considered secondary,formed by replacement of original limestone (CaCO3), andthis dolomitization process is commonly described by the stoi-chiometric equation.

2CaCO3ðlimestoneÞ þMg2þ , CaMgðCO3Þ2ðdolomiteÞ þCa2þ

ð1Þ

Because of the density contrast between calcite and dolo-mite, such mole-for-mole replacement has been linked to anapproximately 13% porosity increase since De Beaumont(1837) first proposed the idea. Alternative reaction stoichio-metries are also likely, with the addition of variable amountsof CO2�

3 leading to porosity occlusion by dolomite overgrowths

or pore-filling cements (Saller andHenderson 2001;Lucia, 2004). Upon burial, a range of processesmay result in preferential preservation of porosityin dolomitized carbonates (Machel, 2004). Thus,the process of dolomitization is a critical controlon reservoir quality and consequent producibility(e.g., Cantrell et al., 2004).

Despite the abundance of dolomite in the rockrecord and dolomite supersaturation of modernseawater, dolomites are rare and occur sparselyinmodern carbonate sediments (Budd, 1997). Dif-ficulties in growing dolomite in the laboratory atnear-surface temperature and pressure (ArvidsonandMackenzie, 1999; Land, 1999) indicate strongkinetic barriers limiting the rate of dolomitizationat low temperatures. Dolomite precipitation doesappear to bemicrobiallymediated under some cir-cumstances (Vasconcelos et al., 1995; Wright andWacey, 2004), and although microbial dolomitesare not generally viewed as volumetrically signifi-cant, they may act as seeds for more pervasive sec-ondary dolomitization. The rate of dolomitizationhas been shown experimentally to be highly de-pendent on several factors, including the Mg:Caratio in solution (Kaczmarek and Sibley, 2007),the mineralogy of the reactant (Gaines, 1974), re-actant surface area (Sibley and Bartlett, 1987),and the presence of kinetic inhibitors, such as sul-fate (Baker and Kastner, 1981). Dolomitizationrate also increases markedly with increasing tem-perature because the kinetic rate constant and themineral saturation state are temperature depen-dent (Arvidson and Mackenzie, 1999). Conse-quently, at elevated temperatures, dolomitizationis likely limited by large-scale mass transport in-stead of reaction rates (Machel, 2004; Whitakeret al., 2004).

The need for an efficient fluid-flow mecha-nism, bywhich reactants and products can be trans-ported to and from the site of dolomitization, ledMachel (2004) to conclude that most models ofmassive dolomitization are essentially hydrologicalmodels. The evolution of these dolomitizationmodels from conceptual cartoons to complex nu-merical simulations was reviewed by Whitaker et al.(2004). This suggested that modeling dolomitiza-tion reactionswithin an evolving flow field is key to

advancing our understanding the formation, na-ture, and distribution of replacement dolomites.This coupled approach has the potential to informus about changes in petrophysical properties, aswell as associated diagenetic reactions such as an-hydrite cementation (Machel, 1986; Lucia, 1999).

Manymassive dolomites appear to formduringearly burial of platform carbonates, sourcing mag-nesium from seawater ormodified seawater (Land,1985). Fluid-flow systems invoked include circula-tion within or below the mixing zone beneath car-bonate islands and reflux of meso- to hypersalinebrines beneath restricted lagoons. However, boththese systems depend upon propitious conditionsat the platform top. For instance, reflux brinescan only form when the platform top is floodedby seawater to shallow depth and are thus vulner-able to changes in relative sea level.

In contrast, geothermal convection, driven bytemperature-controlled variations in fluid density,is essentially independent of relative sea level andwould thus be expected to operate in all platformswith sufficient permeability.Dolomitization is alsofavored by the elevated temperatures resultingfrom geothermal heating. Geothermal convectioncan occur as free or forced convection. Free con-vection is characterized by counterrotating fluidflow cells, which develop in anisotropic carbonateplatforms (Sanford et al., 1998) or those buried bylow-permeability sediments (Wood and Hewlett,1982). However, a substantial bed thickness (300–500 m [990–1640 ft]) free of even minor shalebreaks is required for free convection to occur(Bjorlykke et al., 1988). Furthermore, unless thesefree convection cells are partially hydraulicallyopen (mixed convection of Raffensperger andVlassopoulos, 1999), the available magnesiumwould rapidly be used and dolomitization wouldcease. In contrast, forced convection of cold sea-water through carbonate platforms during earlyburial (also termed Kohout convection) drawson an infinite reservoir of magnesium. Forced con-vection affects large volumes of carbonates for ex-tended periods and appears essentially indepen-dent of relative sea level (Sanford et al., 1998).

Forced convection (henceforth termed geo-thermal convection)was first recognized byKohout

Whitaker and Xiao 891

and coworkers (Kohout, 1965; Griffin et al., 1977)from groundwater temperature profiles in south-ern Florida, which show cooling with depth withinthe limestones and dolomites overlying the CedarKeys anhydrite. Magnesium depletion in watersdischarging from near-coastal shallow springs(Fanning et al., 1981; Schijf and Byrne, 2007) sug-gests that this circulation is driving dolomitization.At a smaller scale, several subsequent studies in-voke geothermal convection to dolomitize late Ter-tiary and Eocene atolls in the Pacific (e.g., Saller,1984; Samaden et al., 1985; Aharon et al., 1987),supported by evidence of negative modern pore-water temperature profiles (LeClerc et al., 1999)and strontium isotope data (Paull et al., 1995).

Inferring the environment, rate, and distribu-tion of dolomitization can be challenging. Evenwhere fluid chemistry indicates dolomitization inmodern geothermal convection systems, subsur-face access is at best partial, and in the absence offluid flux rates, rates of dolomitization cannot bederived. Mathematical models of geothermal con-vection have provided new insights into the rela-tive importance of different fluid-flow drives andthe controls on their operation (Whitaker et al.,2004). For instance, analytical solutions in simpleplatform configurations have suggested that con-vection can occur in the absence of any geothermalheat input driven by the thermal contrast betweencold deep-ocean waters and the warm platformtop (LeClerc et al., 2000) and is best developedat the platform margins unless permeability aniso-tropy is high (Sanford et al., 1998).

Sanford et al. (1998) provided the first sys-tematic numerical analysis of controls on the rateand pattern of geothermal convection and resul-tant temperature distribution in carbonate plat-forms. Platform scale, geometry, and relative sealevel are revealed to be only secondary controls,suggesting that geothermal convection should oc-cur in most active carbonate platforms and alsocontinue after drowning. Declining porosity andpermeability with depth effectively limit signifi-cant fluid flux to the upper 1000 m (3290 ft) ofthe platform, and permeability anisotropy governsthe pattern of convection. Geothermal convectionalso occurs, although more slowly, in carbonate


ramps with shallow basins (Jones et al., 2004).Convection is greatest in the inner part of a homo-clinal ramp but at the break of slope of distallysteepened ramps.

In contrast, explicit modeling of dolomitiza-tion by geothermal convection is in its infancy(Whitaker et al., 2004). Reactive transport model-ing is an emerging technology, which simulatesgeochemical reactions in systems open to ground-water flow (Xu and Pruess, 2001; Steefel et al.,1998). Numerical code couples fluid flow, heat,and solute transport with thermodynamicallyand kinetically controlled reactions. In more ad-vanced codes, these reactionsmodify the composi-tion of fluid and solid phases and also porosity andpermeability, which control subsequent fluid flowand solute transport. Thus, a reactive transportmodel (RTM) can simulate the change in concen-tration of ions in a fluid as a function of dispersiveand advective transport, and also diagenetic reac-tions including dolomitization.

Early RTM simulations of dolomitization sim-ulated geothermal convection over 100 k.y. in anisolatedplatform40 km(25mi) inwidth; suggesteddolomitization was focused in a sweet spot in thedeeper (>1500 m [4930 ft]) platform interior(Wilson et al., 2001). This implied that geothermaldolomitization is not simply a transport-limitedprocess, which would give a distribution mirroringthat of fluid flux, but instead occurs as a gradientreaction along a 60–70°C isotherm where an opti-mum balance between transport and reaction rateexists. In the shallower parts of the platform, convec-tion of seawater provides an ample supply of mag-nesium, but low temperatures appear to limit reac-tion rate; at greater depth, high temperatures favordolomitization but fluid flux limits reaction rate.However, extrapolation of the dolomitization ratefrom these short-term simulations suggests thateven in the most favorable locations, less than 2%dolomite will form in 1 m.y. and complete dolomi-tization will require more than 60 m.y.

Geothermal convection thus appears to be avery slow process, leading to a search for alterna-tive models to explain cases where dolomitizationcan be constrained within a shorter time scale.Jones and Xiao (2005) used an RTM approach

to investigate dolomitization by reflux.Here, evap-oration of seawater at the platform top providesboth the hydrological drive for flow by increasingdensity and generating geochemically favorablefluidswith a highMg2+/Ca2+ ratio, particularly fol-lowing precipitation of gypsum. Simulated rates ofdolomitization depend upon flow rate and brinechemistry and are up to three orders of magnitudefaster than those for geothermal dolomitization pre-dicted by Wilson et al. (2001). The study of Jonesand Xiao (2005) illustrates clearly the importanceof feedbacks between reaction rate, permeability,and fluid flow once significant volumes of dolo-mite are formed.

Many reservoir dolomites are interpreted tobe reflux in origin based on geochemical indica-tors or simply by association with evaporitic condi-tions (Sun, 1995). However, the rock record is fullof dolomites formed at a range of temperatures,which are geochemically indistinguishable fromnormal marine water. Furthermore, it is unwiseto use dolomite geometry or association with sedi-mentary facies to infer the hydrological drive fordolomitization because the spatial distribution ofdolomitization is governed critically by sedimentpermeability and reactive surface area (Wilsonet al., 2001; Whitaker et al., 2004). In this article,we reconsider geothermal convection as a mecha-nism for formation of substantial dolomite bodiesusing an RTMover a time scale ofmillions of years,some two orders of magnitude longer than previ-ous studies by Wilson et al. (2001), and addressfour important sets of questions.

• Can geothermal convection cause significantvolumes of dolomite to form within geologi-cally reasonable time scales?

• If so, do geothermal dolomite bodies have char-acteristic geometries and/or geochemical signa-tures such as temperature of formation?

• To what extent is geothermal dolomitizationcontrolled by the characteristics of the sedi-ments and/or the platform geometry?

• What is the effect on geothermal dolomitiza-tion of syndepositional fractures and faults,which commonly develop along platform mar-gins? Would short-circuiting of convective flow

promote dolomitization by increasing tempera-tures in the interior or focus dolomitization atthe high-flux margins?

METHODS

The field of reactive transport modeling has ex-panded significantly in the past two decades andhas contributed significantly in advancing our un-derstanding ofmany issues inEarth sciences (Steefelet al., 1998).The potential of this technology to im-prove our understanding of carbonate diagenesiswas first demonstrated by Sanford and Konikow’s(1989) partially coupledmodel of dissolutionwith-in the coastal mixing zone of fresh water and saltwater. Fully coupled RTMs have provided consid-erable insights into porosity development duringshallow meteoric (Rezaei et al., 2005) and burialdiagenesis (Jones and Xiao, 2006), dolomitization(Wilson et al., 2001; Jones andXiao, 2005), andde-dolomitization (Ayora et al., 1998).

Geochemical processes are described withinan RTM via the general governing equation

@

@tfCið Þ ¼ @

@xfD

@Ci

@x

� �� fv

@Ci

@x

þ fXk

@Ci

@t

� �k

ð2Þ

where Ci is the concentration of a specific speciesin the pore fluid, D is the combined diffusion anddispersion coefficient, v is the linear fluid-flowrate, and f is porosity. Thus, the change in concen-tration over time is a product of the sum of alltransport processes (diffusion, dispersion, and ad-vection) and the geochemical reactions. The com-plexity of the coupling between transport and re-action terms, together with complex boundaryconditions, requires a numerical solution. Withthe increase in computational power, RTMs havebeen developed that enable simulation of complexgeological systems over extended time scales.Here,we use the numerical program TOUGHREACT(Xu et al., 2004), which is a nonisothermal RTMcapable of simulating multiphase fluid flow, heat,and solute transport with physical and chemical


heterogeneity. An integral finite difference ap-proach is used to obtain space discretization, andflow, transport, and geochemical reactions aresolved separately using a sequential iteration ap-proach (Xu and Pruess, 2001). The code has beenextensively verified against analytical solutions andother numerical simulators (Xu and Pruess, 2001)and applied to a variety of problems (Xu et al.,2006).

Geothermal convection was simulated in atwo-dimensional flow domain representative ofhalf of an isolated carbonate platform, assumingflow is symmetrical. The platform is a rimmedshelf measuring 25 km (15 mi) from the interiorto the margin, with a steep margin sloping into a2000-m (6580-ft)-deep basin. The platform top isflooded with seawater to a depth of 5 m (16 ft).The flow domain is discretized into cells of upto 500-m (1640-ft) width, decreasing to 250 m(820 ft) adjacent to the margin where previousstudies indicate highest fluid-flow rates (Sanfordet al., 1998;Wilson et al., 2001). The vertical thick-ness of the cells ranges from a maximum of 50 m(164 ft) near the base of themodel to 5m (16 ft) inthe upper 50 m (164 ft) of the platform top. Thegrid system thus comprises 4305 active blocks andin the baseline employed linear (Cartesian) coordi-nates. Additional runs were performed using nar-rower and shallower platforms and using a radialgrid to investigate sensitivity to platformgeometry.

The right and left boundaries are specified asno-flow (constant pressure) boundaries, whereasthe lower boundary is closed to flow and solutetransport but open to heat transport, with a speci-


fied heat flux of 60 mW/m2, which is representa-tive of passive margins (e.g., Floridan Plateau;Griffin et al., 1977). The upper boundary, fromthe basin and slope to the platform top, is a fluid-pressure boundary, allowing the recharge or dis-charge of fluids. The temperature along the upperboundary was defined from depth below sea levelafter Sanford et al. (1998). Initial temperature dis-tribution reflects advective heat transport by geo-thermal convection prior to initiation of any re-actions. Although effective thermal conductivitywill vary slightly with mineralogy and porosity,TOUGHREACT does not at present include thesefeedbacks. A uniform and constant thermal con-ductivity of 2.2W/m °C was specified, with a spe-cific heat capacity of 1000 J/kg °C.

The initial porosity specified is an exponentialfunction of depth (equation 3) based on core datafor Cenozoic and Mesozoic carbonates from theFlorida platform (Schmoker and Halley, 1982).

f ¼ 0:4173e�z=2498 ð3Þ

where f is the fractional porosity and z is thedepth below sea level (in meters). Permeability isderived from porosity based on relations derivedfrom Lucia’s (1995) analysis of core-scale mea-surements for a range of limestone and dolomiterock fabrics (Table 1). Three separate grain-size-dependent classes are identified; the class 2 rela-tionship is used in most simulations, but the sen-sitivity to porosity-permeability relationship isexplored using class 1 and class 3 relationships.The resulting permeabilities (Figure 1) vary over

Table 1. Porosity-Permeability Relations of Different Classes of Carbonate Rock Fabric Compiled from Lucia (1995)*

Rock Class
Rock Fabric Grain Size (mm) Porosity-Permeability Relationship
Class 1
Limestone and dolomitized grainstones;large crystalline grain-dominated dolopackstones
>100
k = (45.35 � 108) � f8.537
Class 2
Grain-dominated packstones; fine- to medium-grain-dominated dolopackstones; mediumcrystalline mud-dominated dolostones
20–100
k = (2.040 � 106) � f6.380
Class 3
Mud-dominated limestones; fine crystallinemud-dominated dolostones
<20
k = (2.884 � 103) � f4.275
*k is the maximum (horizontal) permeability in millidarcies (1 md = 10−15 m2); f is the fractional porosity.

up to four orders ofmagnitude for any one rock fab-ric class over the simulated depth range (0–3 km[0–1.8 mi]). Permeability anisotropy (khorizontal:kvertical) arises from heterogeneities in rock properties.At core scale, horizontal permeability in lime-stones and dolomites can average 10–1000 timesthe vertical permeability (e.g., McNamara andWardlaw, 1991; Amthor et al., 1993). Permeabil-ity anisotropy tends to increase with the scale ofobservation (Haldorsen, 1986), arising predomi-nately from sedimentary layering, as well as earlydiagenesis. In this study, the initial permeabilityanisotropy was specified as 1000 based on the re-sults of flow-based scale-up simulations (Jones,2000).

Temporal changes in porosity and permeabil-ity that result frommineral dissolution and precip-itation can modify fluid flow. Fluid-rock inter-actions were ignored in the short-term reactiontransport simulations of geothermal dolomitiza-tion by Wilson et al. (2001) because only minoramounts of dolomite (<0.003 volume fraction)

were formed.However, simulations of reflux dolo-mitization over 1 m.y. by Jones and Xiao (2005)demonstrated how incorporation of transport-reaction feedbacks significantly modified the dis-tribution of diagenetic alteration. The correlationbetween porosity and permeability is very com-plex because of the interplay of many factors, in-cluding pore-size distribution, pore geometry, andconnectivity. Furthermore, the degree and mannerin which dolomitization affects the relationship be-tween porosity and permeability are highly vari-able. Mimetic dolomites can exhibit a remarkabledegree of preservation of sedimentary texturesand by implication porosity-permeability, but de-positional fabrics can be completely destroyed forexample in sucrosic dolomites (Lucia, 2004). Inthis study, we used a simplified Carmen-Kozenyequation (equation 4) (Bear, 1972) to modifypermeability.

kj ¼ ki1� fið Þ2

1� fj� �2

fjfi

� �3

ð4Þ

where k is permeability (in square meters), f isporosity, and i and j are the previous and subse-quent time steps. This equation ignores the effectsof changes in grain size, tortuosity, and specificsurface area.

Our geochemical calculations include 9 pri-mary and 26 secondary aqueous species and 3min-eral species (Table 2). The initial mineralogy ofthe flow domain is specified to be 99% calcite,with 1% seed dolomite representing minor syn-depositional dolomitization and providing nucle-ation sites. In addition, anhydrite is incorporatedas a secondary mineral. Mineral volumes are pre-sented here as fractions of the solid rock volume(totaling unity).

The initial fluid composition is specified as sea-water modified to equilibrium with respect to cal-cite but remaining supersaturated with respect todolomite (Table 3) to represent early diagenesisduring very shallow burial. This has been docu-mented in both modern (Morse et al., 1985; Rudeand Aller, 1991) and ancient settings (Hendry et al.,1995; Cherns and Wright, 2000), evidenced by

Figure 1. Relationship between permeability and depth belowthe platform top based on the Schmoker and Halley (1982) po-rosity depth curve for Florida and the porosity-permeability re-lationships of Lucia (1995).


aragonite dissolution and/or replacement by cal-cite. Although some carbonate pore waters showevidence of sulfate reduction driven by oxidationof organic carbon, these reactions are not simu-lated here.

Dolomitization is assumed to occur via calcitedissolution followed by dolomite precipitation(Machel, 2004). High-temperature experimentsreveal dolomite crystals growing on the edges andcorners of calcite substrate characterized by disso-lution etch pits (Kaczmarek and Sibley, 2007). Giv-en that the rate of dolomitization is several ordersof magnitude slower than that of calcite dissolu-tion and anhydrite precipitation, both calcite andanhydrite are assumed to be thermodynamic min-erals (Table 4). Thus, we model calcite dissolu-tion as a thermodynamic process, with the rateof dolomitization controlled by the rate of dolo-


mite precipitation, which is modeled as a kineticprocess. This avoids the need for specification ofthe stoichiometry of the dolomitization reaction.Furthermore, it enables the use of the kinetic ex-pression for dolomite precipitation of Arvidson andMackenzie (1999) (equation 5), consistent withprevious reaction transport modeling of dolomiti-zation (Wilson et al., 2001; Jones and Xiao, 2005).

rdol ¼ AsAe�EaRTð Þ 1� Q

Keq

� �2:26

ð5Þ

where rdol is the reaction rate of dolomite precip-itation, As is the specific reactive surface area, andtogether, Q, the activity quotient, and Keq, theequilibrium constant for ordered dolomite, de-fine the saturation index. The rate constant as de-fined from laboratory experiments where A, thepreexponential factor, is 11.22mol/cm2; Ea, the ac-tivation energy, is 1.335 � 105 J/mol; R is the uni-versal gas constant; T is temperature (K); and 2.26is the reaction order.

Table 3. Initial Fluid Composition at 25°C

Component
Total Aqueous
Concentration (mmol/kg)

Na+
480 Mg2+ 54.0 Ca2+ 9.00 K+ 10.0 Cl− 560 SO�2
4
28.0 HCO�
3
0.700 pH 8.2
Table 4. Dissociation Constants (Log[K] to the Base 10) at 25°C
for the Three Mineral Species Simulated
Mineral
Log(K) at 25°C
Calcite
1.849 Dolomite 2.514 Anhydrite −4.306
Table 2. Aqueous and Solid Species Included in Reactive Transport Simulations of Geothermal Convection

Primary Aqueous Species
Na+ Ca2+ Mg2+ K+ H+
Cl−
SO2�4 HCO�
3
H2O
Secondary Aqueous Species
CaCl+ CaCl2(aq) CaCO3(aq) CaHCO+
3
CaOH+
CaSO4(aq)
CO2(aq) CO2�3 H2SO4(aq) HCl(aq)
HSO�4
KCl(aq) KHSO4(aq) KOH(aq) KSO�
4
Mg4(OH)
+44
MgCl+ MgCO+
3
MgOH+ MgSO4(aq) NaCl(aq) NaCO�
3
NaHCO3(aq) NaOH(aq) NaSO�4 OH−
Mineral Species
Calcite Dolomite Anhydrite

This rate law provides a route by which kineticand thermodynamic principles can be integratedand experimental results can be extrapolated tonatural processes. The rate constant in equation3 is derived from experiments of Arvidson andMackenzie (1999), which precipitated nonstoi-chiometric dolomite (55–58mol%CaCO3) at ele-vated temperatures (115–196°C). One importantuncertainty of this study is the extrapolation ofthese results to temperatures less than 100°C. Lab-oratory rates of dolomitization are also acceler-ated by increasing the ratio of mineral surface areato reactor volume and running experiments farfrom equilibrium. In contrast, waters in naturalsystems tend toward equilibriumwhere uncertain-ties in rate constants are greatest (Bethke, 2008).Although no theoretical framework exists inwhich to extrapolate from high-temperature lab-oratory studies, recent work by Kaczmarek andSibley (2007) indicates that high-temperature syn-thetic dolomites and low-temperature natural do-lomites form by the same mechanism. Further-more, Arvidson and Mackenzie (1997) found aremarkable consistency between rates of dolomiti-

zation in the modern Persian Gulf and Pliocene–Pleistocene Gulf of California estimated from lab-oratory rate data and independent estimates madefrom field observations.

Although the rate of reaction at a mineral sur-face is governed by free energy, it is commonly ap-proximated by the reactive surface area exposed todiagenetic fluids (Gaines, 1980; Sibley and Bartlett,1987). Our baseline simulations assume a specificreactive surface area of 1000 cm3 (61 in.3)/g, whichequates to a sediment with an average diameter ofidealized grains of 50-mmdiameter (Lichtner, 1996).Geometric estimates may underestimate surfacearea, particularly for biotic grains with complex ge-ometries and intragranular porosity (Walter andMorse, 1984). However, mineral surfaces can alsobe shielded with oxide, hydroxide or organic coat-ings, contact with organic matter, and other grainsand cements (Cubillas et al., 2005; Perry and Taylor,2006). The evolution of reactive surface area duringburial due to diagenesis, including dolomitizationand compaction, remains a source of uncertainty.

Within TOUGHREACT, an automatic time-stepping scheme is implemented,whichdiscretizes

Table 5. Parameters Controlling Geothermal Convection, Baseline Value, and Range of Values Tested in Sensitivity Analysis

Parameter
Baseline Range
Whitak

Figures*

er and Xiao
89
Platform GeometryPlatform thickness (km)
3 km 1, 2 km 5 Platform width (km) 25 km 2.5, 10 km 6 Platform shape Linear Radial 7
Boundary Conditions
Geothermal heat flux 60 (mW m−2) 40, 100 (mW m−2) 8 Relative sea level Flooded to 3 m Exposed, drowned to 500 m 9
Sediment Properties
Effective reactive surface area 103 cm2 g−1 102, 104 cm2 g−1
Permeability-depth relationship**
Class 2 Class 1, class 3 10 Permeability-depth and RSA** Class 2 103 cm2 g−1 Class 1 and 102 cm2 g−1,
class 3 and 104 cm2 g−1
10
Permeability and RSA layering**
No layering 50-m beds class 1 and 102 cm2 g−1,50-m beds class 3 and 104 cm2 g−1
11

Fractured margin
No fracturing 2-km-deep fracture open to seabed,1.5-km-deep fracture closed > 0.5 km
12

*Baseline illustrated in Figures 2, 3, and 4.**See Figure 1 and Table 1. RSA = reactive surface area.

7

time based on the convergence rate of the iterationprocess. Dolomitization driven by geothermal cir-culation was simulated to 30 m.y. in the baselineand 15 m.y. in the sensitivity analyses, with initialtime steps of 62.5 yr, stabilizing to 1000 yr after0.3m.y. Parameters tracked include changes in flowvelocity and temperature, aqueous and solid spe-cies (Table 2), reaction rates and saturation stateswith respect to minerals of interest (Table 4), andporosity and permeability. We systematically in-vestigate controls on the distribution of dolomiti-zation driven by geothermal convection, includingplatform geometry, boundary conditions, sedimentreactive surface area, and permeability (Table 5).

RESULTS

Significant Dolomitization Driven byGeothermal Convection

The fluid-flow and heat-transport systems simu-lated in the early stages of this simulation are con-sistent with those in previous studies of compa-rable rimmed shelf carbonates dominated by grainypackstones (Sanford et al., 1998; Wilson et al.,2001; Jones et al., 2004). Cold ocean water entersalong the platform slope and flows laterally and up-ward to discharge from the platform top (Figure 2).Fluid-flow velocities are greatest in the upper plat-form adjacent to the margin. The depth depen-dence arises from the initially specified reductionin permeability with depth (Figure 1), whereas


the lateral penetration arises from the high anisot-ropy of the layered carbonates. Over time, dia-genesis progressively modifies the porosity andpermeability (discussed in more detail below), en-hancing fluid flow and also advective cooling.Temperatures reflect advection of cool seawaterthrough the platform in response to basal heatingand thermal contrasts between the platform topand the ocean boundary (Figure 2). Cooling ex-tends across most of the platform, with a tongueof less than 20°C water extending progressivelyfrom the platformmargin over time, but ascendingwaters result in limited advective warming of theplatform interior. Shallow fluids tend to 25°Cdue to thermal conduction downward from theflooded platform top.

Figure 3 tracks temporal development of thedolomite body generated by this geothermal con-vection from 0.1 m.y. when the amounts of dolo-mite are less than 0.4% to 30 m.y. when largeparts of the platform are completely dolomitized.Dolomite forms within two distinct zones that de-velop at different rates, which over time merge tocreate a single dolomite body. A volumetricallysignificant broad inclined dolomite ellipse paral-lels the isotherms, shallowing with distance fromthe margin. In this first zone, temperatures aresufficient to enhance reaction rate whereas masstransport rate is also adequate to supply magne-sium and remove calcium. Toward the platformmargin, fluid-flow rates are highest but low tem-peratures (<20°C) limit reaction rates at mostdepths. Dolomite initially forms at shallow depth

Figure 2. Baseline simulationresults after 0.1, 15, and 30m.y. forfluid flux (showing representa-tive streamlines) and temperature.

close to themargin very slowly, but after more than10 m.y., reaction rates accelerate and the lower do-lomite zone extends toward the platform margin.Dolomitization does not occur at depths greaterthan approximately 2000 m (6580 ft) where fluidflux is limiting, nor in the platform interior due toupstream depletion of magnesium. A secondmoretabular-shaped dolomite zone develops at shallowdepth (<300–400 m [984–1312 ft]) and is limitedto within 10 km (6 mi) of the platform margin upto 15 m.y. but later extends farther toward the in-terior. Reactions are most rapid at the shallowestpart of the platform immediately adjacent to themargin where dolomite forms due to the very highflux of seawater close to 25°C.

Both the rate and pattern of dolomitizationevolve through time due to important feedbacksbetween fluid and solid composition and conse-quent changes in permeability, which determinesfluid flow and thus mass flux rates. The deeper el-liptical dolomite zone extends initially toward theplatformmargin and the source ofmagnesium. Ex-tension toward the platform interior occurs at shal-lower depths and is more rapid once upstream do-

lomitization nears completion. This is caused by acombination of increased flux ofmagnesium to theinterior and higher flow rates in the increasinglypermeable dolomitized part of the platform, andoccurs despite greater advective cooling. The shal-lower tabular dolomite zone extends progressivelyto merge with the developing ellipse. Even after30 m.y. when large parts of the dolomite body arecompletely dolomitized, the transition from com-pletely dolomitized to undolomitized rock occursover a vertical distance of 200–300 m (660–990 ft)and horizontally over 1000–2000m (3290–6580 ft)instead of forming a sharp reaction front.

At an early stage, the total amount of dolomiteformed by geothermal convection is very minor.Extrapolation of rates from short-term (0.1 m.y.)RTM simulations by Wilson et al. (2001) suggeststhat complete dolomitization requires a minimumof 50–60 m.y., and thus geothermal convectioncould not be responsible for formation of manymassive dolomite bodies where the available timewindow is considerably narrower. Our more ex-tended simulations reveal important nonlinearitiesin the rate of dolomitization, with an increase in

Figure 3. Distribution of dolo-mite as a fraction of rock volumepredicted in the baseline simu-lation at time steps from 0.1 to30 m.y. Note the 10 times ad-justment in scale bar from the0.1- to 2.5-m.y. images com-pared to those for the 5–30-m.y.time steps.


reaction rate as dolomite abundance increases, giv-ing complete dolomitization locally within 5 m.y.and over significant areas of the platform in 10–15 m.y. This is consistent with high-temperatureexperimental results, which show that once thedolomitization reaction starts, it proceeds veryquickly (Kaczmarek, 2005).

The distribution of calcite mirrors that of dolo-mite (Figure 4), but the mole:mole replacementof calcite by the denser dolomite creates porosity.Thus, from an initial exponential decline in po-rosity with depth at the start of the simulation,porosity is enhanced by up to 13% within the do-lomite body. In the shallower zone, complete do-lomitization is followed by precipitation of somedolomite cement (overdolomitization), reducingporosity by up to 3% near the platform margin.In the platform interior, a smaller inclined zoneat 1000–2000 m (3290–6580 ft) depth down-flow of the 50°C isotherm is observed, where po-rosity is reduced by up to 7.5% due to precipitationof calcium sulfate (most likely at this pressure and


temperature as anhydrite). Anhydrite precipita-tion is a direct consequence of dolomitization,which enriches fluids in aqueous calcium, and theabundance of sulfate from seawater, as also notedby Wilson et al. (2001). Anhydrite precipitationthus occurs where sufficiently high temperaturesoccur downstream of the dolomitization zonewhere calcium mass flux is also favorable. Anhy-drite precipitation rate is initially rapid, approxi-mately half that in reflux simulations (Jones andXiao, 2005) despite themuchhigher sulphate con-centration of brines. However, the reaction thenbecomes self-limiting with progressive reductionof fluid flow due to the reduction of porosity andpermeability.

The changes in porosity are reflected in changesin permeability (Figure 4). Complete replacementdolomitization increases sediment permeability upto 7.5� 10−12 m2 (7.5 d) near the platform top dueto porosity-permeability feedbacks approximatedusing a simplified Carmen-Kozeny equation. Simi-larly, a reduction in permeability fromminor shallow

Figure 4. Distribution of dolomite, calcite, and anhydrite as a fraction of rock volume predicted in the baseline simulation after 30 m.y.Porosity and permeability are shown at the start of the baseline simulation and after 30 m.y. and compared in terms of the change inporosity over 30 m.y.

overdolomitization and, most markedly, anhydriteprecipitation is observed. The porosity-permeabilitycoupling reduces the depth of maximum fluid flowand advective cooling of the platform over thecourse of the simulation (Figure 2).

Whereas mineralogy and porosity are the netproduct of diagenesis at all previous times, fluidcomposition reflects reactions occurring at a giventime, as well as recent upstream reactions. Plots ofmagnesium, calcium, sulphate, and pH are given inDatashare Figure 1 (see AAPG Datashare 36 atwww.aapg.org/datashare). Replacement dolomiti-zation leads to magnesium depletion of up to 45mM magnesium in the fluids and molar equivalentenrichment of calcium. The low magnesium/cal-cium of fluids reaching the platform interior limitsdolomitization despite favorable temperatures.Although most carbonate for dolomitization issupplied by calcite dissolution, giving net porositygeneration, the reduction in pH suggests thatsmall amounts of carbonate are also sourced fromthe fluid. The elevated calcium resulting from do-lomitization enables anhydrite precipitation to oc-cur where temperatures exceed 50°C, reducingconcentrations of both calcium and sulphate inthe platform interior. In zones where dolomitiza-tion is complete, the zone of overdolomitization,very minor (∼0.001 mM) reduction in magnesiumand calcium is observed due to small volumes ofdolomite precipitated per unit volume of fluid.

This RTM simulation suggests that geother-mal convection can generate substantial dolomitebodies within a geologically reasonable time scale.Given that geothermal convection is mostly inde-pendent of relative sea level (Sanford et al., 1998),geothermal dolomitization of carbonate platformsduring shallow burial would be expected to be ubiq-uitous. Many platforms remain mostly or entirelyundolomitized, and thus the question becomes,why do many carbonate platforms remain calciticduring early burial? To address this, we investigatedthe sensitivity of predictions of geothermal dolomi-tization to several important controls in a series of15-m.y. simulations, which are variants of the base-line simulation described above.

Platform Geometry: Platform Thickness, Widthand Shape

Carbonate platforms develop in a variety of topo-graphic and tectonic settings and consequently rangein geometry and scale. The baseline simulation isbroadly comparable to the Cretaceous to Modernplatforms of the Bahamas and Florida (Melim andMasaferro, 1997) or theCarboniferous of the northCaspian (Weber et al., 2003).However,many otherplatforms are thinner and exhibit lower relief rela-tive to the basin. Simulationswere runwith the plat-form thickness reduced to 1500 and 750 m (4930

Figure 5. Reduced platformthickness simulation results forfluid flux (showing representa-tive streamlines), temperature,and dolomite as a fraction of therock volume after 15 m.y. forplatforms 1500 and 750 m (4930and 2470 ft) thick.


and 2470 ft) (Figure 5) while maintaining the plat-form slope angle. Geothermal convection appearsto operate with at least equal vigor in shallower plat-forms, with higher maximum flow velocities. Theresultant increased advective cooling inhibits an-hydrite formation in all but the lowest part of the1500-m (4930-ft) platform. However, dolomitiza-tion occurs rapidly; by 15m.y., the entire thicknessof both platforms is completely dolomitized in azone extending inward from themargin. In the shal-lowest platform, the dolomite front extends towardthe interior at a rate of approximately 1 km (0.6mi)/m.y., although the inner 1–2 km (0.6–1.2 mi) re-mains calcitic even after 30m.y. As in the baseline,the model predicts the formation of geothermaldolomite at low temperatures providing sufficientmass flux.


Platformwidth can range froma fewkilometers,for example, where platforms nucleate on narrowridges or fault blocks, to shallow shelf (epeiric) seasextending several hundreds of kilometers. Hydro-logical modeling (Sanford et al., 1998) indicatesthat platform width is a secondary control on thetotal fluid flux, with lower flux driven by geother-mal convection in narrowplatforms and reduced ad-vective cooling. We ran RTM simulations for plat-forms with a half width of 2.5 and 10 km (1.5 and6 mi) compared to the 25-km (15-mi) half-widthbaseline simulation (Figure 6). The maximum flowvelocities for all three simulations were similar, butthe area affected by high flow reduces in propor-tion to platform width. Consequently, tempera-tures at a given distance from the margin are higherin the narrower platforms, although the maximum

Figure 6. Variable platform width simulations for fluid flux (showing representative streamlines), temperature, and dolomite as a fractionof the rock volume after 15 m.y. for platforms 2.5 and 10 km (1.5 and 6 mi) wide compared to the 25-km (15-mi) baseline platform.

temperature is some 40°C cooler than that in thebaseline simulation. Given these temperatures, an-hydrite formation was insignificant but dolomiti-zation remained active in the narrower platforms,with both showing complete dolomitization ofmost of the upper 750 m (2461 ft).

The baseline platform is simulated using pla-nar (Cartesian) coordinates, meaning that we as-sume the platform is long and has infinite bound-aries. Platforms with a length:width ratio of morethan 4–5 approximate an infinite strip (Vacher,1988) and commonly develop attached to landmasses and along linear features as fault blocks.However, many isolated platforms exist as quasi-circular features, and in these cases, flow circula-tion may be essentially radial. Geothermal con-vection in a circular platform was simulated using

radial coordinates (Figure 7) for platforms of 2.5-,10-, and 25-km (1.5-, 6-, and 15-mi) radius. Flowenters the circular platform from the entire cir-cumference of the margin and converges towardthe platform interior. Flow rates over much ofthe platform are significantly lower, resulting inless advective cooling and a considerably reducedvolume of dolomite. The shape and abundance ofdolomite formed over 15 m.y. in the radial sim-ulations resemble that of the linear coordinate sim-ulations after only 1.5 m.y.

Boundary Conditions: Geothermal Heat Flux,Platform Exposure, and Drowning

Specification of appropriate boundary conditionsis critical in any modeling exercise to ensure that

Figure 7. Radial simulations of platforms with varying radii showing results for fluid flux (including representative streamlines), tem-perature, and dolomite as a fraction of the rock volume after 15 m.y.


the resulting simulation approximates the behav-ior of natural systems. Here, the fundamentaldrive for fluid circulation is the temperature con-trast between the geothermally warmed platforminterior and the cold ocean waters. In the baselinesimulation, we used a value for geothermal heatflux of 60 m W/m2, but sensitivity to natural var-iations in heat flux for different crustal terrainswas investigated in simulations with a heat fluxof 100 and 40 mW/m2 (Figure 8). Reducing theheat flux to 40 mW/m2 has only a very minor im-pact on fluid flux, although the deeper part of theplatform interior is cooler by up to 30°C. At theselower temperatures, no anhydrite is formed, andthe main elliptical dolomite body develops at aslower rate (approximately half that of the base-line simulation). Similarly, increasing heat flux to100mW/m2 has little effect on fluid flux, but tem-peratures are significantly higher throughout theplatform. The dolomite ellipse develops in thesame location, confirming the dominant controlby flux, but the higher temperatures here acceler-


ate dolomitization rate, so that by 15 m.y., the ex-tent of the dolomite body approaches that seen inthe 30-m.y. baseline simulation. In addition, thehigher temperatures extend both the area of anhy-drite formation and the reaction rate, so by 15m.y.,anhydrite approaches 11% of the total rock fractionwith concomitant reduction in porosity. The shal-low tabular dolomite body is unaffected by changesin basal heat flux.

The upper boundary of the platform is vulner-able to changes in relative sea level, which are re-corded by changes in depositional facies, subaerialexposure surfaces, and marine hardgrounds. Thethermal contrast between platform top and basin,which drives convection, is significantly reducedby platform drowning, whereas emergence willlead to development of ameteoric water circulationsystem.Here, we consider the effect of platform topexposure and also platform drowning on dolomi-tization by geothermal convection (Figure 9), butwe do not consider interactions between geother-mal, meteoric, and/or reflux circulation (see the

Figure 8. Effect of basal heatflux on geothermal convectionand resultant dolomitizationillustrated for a heat flux of 40and 100 mW/m2 for fluid flux,temperature, and fraction ofdolomite and anhydrite after15 m.y.

Discussion section). Our baseline simulation as-sumed a shallow depth (3m [10 ft]) of normal sea-water at 25°C across the platform top. Emergenceis simulated by specification of a no-flow boundaryacross the platform top to replicate the effect of thedevelopment of a shallow cap of meteoric waterspreventing discharge from the platform top. A sim-ilar system would result from deposition of a verylow permeability cap of mud over the top of theplatform. This results in reversal of flow directionin the upper 400–500 m, with fluids forced to dis-charge from the upper platform slope. The longerflow path reduces fluid flux to about half that ofthe baseline simulation, with consequent reduc-tion in advective cooling. Formation of a shallowdolomite body is inhibited by platform top expo-sure, and the reduced fluid flow slows the rate ofdolomitization at depth, producing a chevron-shaped dolomite body. For the platform drownedby 500m (1640 ft) of ocean water, the platform toptemperature was set at 15°C. Whereas the pattern

of fluid flow resembles that of the baseline simu-lation, the reduction in the thermal contrast be-tween the platform top and the deep ocean halvesthe fluid flux and reduces platform temperatures.Dolomitization rates are significantly reducedboth in the shallower marginal dolomite bodyand the deeper ellipse where less than 55% dolo-mite after 15 m.y. is observed. Because of the re-duced fluid flux, anhydrite precipitation is re-duced in both the emergent and particularly thecooler drowned platform.

Sediment Properties: Reactive Surface Areaand Sedimentary and Fracture Permeability

The rate of diagenesis reflects the mineral reac-tive surface area and the mass of mineral available(Steefel andVanCappellen, 1990; Bethke, 2008),as demonstrated by the accelerating rates of dolo-mitization seen in our simulations (Figure 3). Weassume 1% seed dolomite, compared with the 0.3%

Figure 9. Emergent anddrowned platform simulationresults for fluid flux, temper-ature, and fraction of dolomiteand anhydrite after 15 m.y.


used byWilson et al. (2001), and thus at very earlytimes, dolomitization proceeds more rapidly in oursimulations, most noticeably in areas where dolo-mitization rates are slower. Over a longer simula-tion time, the effect of a more than three orders ofmagnitude variation in dolomite seed (from 0.01%to 3%) is relatively minor but most obvious nearthe platform margin below approximately 500 m(1640 ft) where the reaction rate is temperaturelimited (Datashare Figure 2; see AAPG Data-share 36 at www.aapg.org/datashare).

The reactive surface area was varied from thebaseline value of 103 cm2 g−1 over the entire area byplus or minus one order of magnitude, with con-siderable impact on the predicted rate of dolomi-tization (Figure 10). Comparisons are initially


made for the packstone-wackestone baseline plat-form (class 2 poroperm transform; Figure 10 centercolumn). Dolomitization of more reactive sedi-ments is faster, fluid flux is the dominant controlon dolomite distribution, and the reaction front ismuch sharper. The zone of complete dolomitiza-tion extends to the platformmargin, including areaswhere temperatures are less than 10°C. Dolomi-tization of less reactive sediments is slower, partic-ularly at shallow depth, and after 15 m.y., no areasof complete dolomitization are observed. Thedistribution of the dolomite reflects a balance be-tween fluid flux and temperature, favoring deeperdolomitization. The isotherms and fluid flow aremodified slightly as a result of changes in perme-ability due to dolomitization (results not shown).

Figure 10. Reactive surface area and permeability-depth simulation results for fraction of dolomite after 15 m.y., with fluid flux andtemperature shown for different permeability-depth relationships for the baseline reactive surface area (103 cm2 g−1) only.

The porosity and permeability of platformcarbonates are characteristically variable both lat-erally and in particular vertically due to variationsin primary depositional texture and secondarydiagenetic alteration. To understand the effect ofdepth variation of permeability, we ran a simulationusing Lucia’s (1995) class 3 and class 1 porosity-permeability relationships (Table 1, Figure 1) devel-oped respectively for permeable mud-dominatedlimestones and fine-grained (<20 mm) dolostonesand more permeable grainstones and large dolo-mite crystals (>100 mm). The latter failed to con-verge because of high flow rates, and thus perme-ability was reduced to one order of magnitudehigher than class 2. Initially, the reactive surfacearea was maintained at 103 cm2 g−1. In the high-permeability platform (Figure 10, left column),the fluid flux is up to one order ofmagnitude greaterthan in the baseline simulation for medium-grained(20–100 mm) sediments, resulting in widespreadand significant platform cooling. An elliptical do-lomite body can still be recognized, occurring ata greater depth, inclined at a shallower angle (re-flecting the isotherms), and forming at rather coolertemperatures (<30°C) than in the baseline simu-lation. In contrast, the shallow tabular dolomitebody is more extended, entirely dolomitizing theupper 500–600 m (1640–1968 ft) of the platformover 15 m.y. At these low temperatures, no anhy-drite cements are precipitated. Fluid flux in thelow-permeability platform (Figure 10, right col-umn) is reduced by some two orders of magnituderelative to the baseline simulation, and tempera-tures are almost entirely conductive. Because ofthe low flux, dolomitization is only partial (<70%)after 15m.y. and is restricted to a narrow zonewith-in 2 km (1.2 mi) of the margin where temperaturesare mostly less than 30°C. Despite higher tempera-tures in much of the low-permeability platform,rates of dolomitization do not increase calcium con-centrations sufficiently to generate much anhydriteprecipitation (maximum <1%).

Although varying the reactive surface area orpermeability-depth individually reveals the man-ner in which each controls the hydrochemical sys-tem, in nature, these two parameters are likely tocovary because of the strong grain-size control

on the reactive surface area. Geometric consider-ations suggest that the reactive surface area is in-versely proportional to the average grain diameter.Fine-grained sediments thus tend to be both lesspermeable and have a higher reactive surface area,forming dolomites that are characteristically ofsmaller grain or crystal size. In contrast, coarse-grained sediments are both more permeable andhave a lower reactive surface area. A muddy plat-form was simulated using a high reactive surfacearea of 104 cm2 g−1 and a depth-dependent perme-ability characteristic of Lucia’s (1995) class 3 rockfabric. Fluid flux and temperature were almostidentical with the class 3 permeability-depth casedescribed above, and although the zone of dolomi-tization is similarly restricted in area, the abundanceof dolomite within this zone is higher. In a grainyplatform with a reactive surface area of 102 cm2

g−1 coupled with depth-dependent permeability10 � Lucia’s (1995) class 2 rock fabric, dolomiti-zation is significantly reduced compared to boththe baseline and the high-permeability, moderatereactive surface area simulations (Figure 10). Be-cause of the strong control of reaction rate by tem-perature at low dolomite abundance, the advectivecooling of the more permeable platform generatesan elliptical body of partial (<50%) dolomite in theinterior of the platform and only a very thin skin ofshallow dolomite.

The environmental conditions and thus deposi-tional regimes, which typifymany carbonate plat-forms, are commonly temporally variable.Withinthe upper 2 km (1.2 mi) of the platform, we simu-lated a simple vertically stacked sequence, alternat-ing 150-m (492-ft)-thick units of class 2 (packstone-wackestone) sediments with a 103 cm2 g−1 reactivesurface area, and 50-m (164-ft)-thick layers of eitherlow-permeability but more reactive (muddy) sedi-ments or high-permeability, less reactive (grainy)sediments (Figure 11). Although in each bed thepermeability anisotropy is maintained at 1000, thisinterbedding increases effective anisotropy at theplatform scale. With the introduction of muddylayers, fluid flux is significantly reduced comparedto the baseline, reducing advective cooling of theplatform. By 15 m.y., dolomitization is completewithin 4 km (2.4 mi) of the margin in this high


flow zone, and at shallow depth, tongues of dolo-mite extending toward the interior are developedpreferentially within the more reactive, less per-meable beds. With increasing depth, the perme-ability of both sediment types decreases, andthis is mirrored by the fluid flux. Below 600 m(1968 ft), fluid flux is insufficient to dolomitizethe muddy layers and occurs only within the morepermeable class 2 sediments. A minor amount(<4%) of anhydrite forms at depths greater than1 km (0.6 mi) within a limited zone downstreamof the platform-margin dolomites around the 60°Cisotherm and only in the class 2 sediments.

A very different pattern of fluid flow, tempera-ture, and dolomitization results from the specifica-tion of grainy layers (Figure 11). These effectivelypirate the flow, with very high fluxes (>50 m.y.−1

adjacent to the margin), which exceed those inthe homogeneous grainy platform (Figure 10).However, fluxes within the class 2 sediments areone order of magnitude lower than in the baselinesimulation. Flow in the higher permeability layerssignificantly cools the platform, and conduction pre-


vents any vertical temperature stratification. Theresulting pattern of dolomitization shows markedlayering, with complete dolomitization of almostall class 2 sediments in the upper 600 m (1968 ft)of the platform. Although fluid flux rarely exceeds0.4 m.y.−1, in these sediments (as in the platformwith muddy layers), the more reactive sedimentsdolomitize preferentially given sufficient fluid flow.At depths of 600–1600 m (1968–5249 ft), dolo-mitization continues to favor the more reactiveclass 2 sediments, but within each class 2 layer, do-lomite abundance increases with depth as magne-sium is sourced from the underlying class 1 layer.Below 1600 m (5249 ft), the class 2 sediment per-meability has reduced sufficiently so that dolomiti-zation occurs preferentially within the grainy layersdespite their lower reactive surface area.

In many carbonates, fracturing is also an im-portant factor in determining the structure of per-meability, providing predominantly vertical baf-fles to or conduits for fluid flow. Margin-parallelfracture systems characterize many modern andancient carbonate platforms, particularly those

Figure 11. Simulation resultsfor fluid flux, temperature, andfraction of dolomite and anhydriteafter 15 m.y. in Class 2 103 m2 g−1

platform with lower permeabil-ity (Class 3), more reactive(104 m2g−1) muddy layersand with higher permeability(Class 1), less reactive (102 m2 g−1)grainy layers.

Figu

re12

.Simulationresults

forfluidflux,temperature,and

fractionofdolomite

after15m.y.inplatform

swith

2-km

[1.2-mi]-deep,100-m

(328-ft)-w

ideverticalfracturezone

set1

km(0.6mi)inboardof

themargin,

within

which

perm

eability(kf)isiso

tropicandseta

sadepth-dependentfractionof

theverticalorhorizontalp

ermeabilityof

theclass

2platform

sediments(kvandk h,respective

ly).


accumulated during icehouse periods (e.g.,Whitakeret al., 1997;Weber et al., 2003; Baceta et al., 2007).Bank-marginal fractures develop by a range of pro-cesses associated with oversteepening of aggra-dational platform margins (Smart et al., 1987)or reef progradation over softer slope sediments(Hunt et al., 2002). These fractures are character-istically near vertical, commonly with little offset,but may be enlarged by early diagenetic (karstic)processes or partially infilled with surface-derivedsediments or cements (Smart et al., 1987; Kosaand Hunt, 2006). In modern platforms, bank-marginal platforms significantly impact the hy-drology of diagenetic fluids (Whitaker and Smart,1997) and resulting dolomitization (Whitaker et al.,1994).

In simulations to illustrate the impact of bothsealed and open fractures, we specify a 100-m(328-ft)-wide fracture zone some 1 km (0.6 mi)inboard of the margin extending from the plat-form top to 2-km (1.2-mi) depth (Figure 12).Within the fracture zone, porosity is independentof depth and permeability is assumed to be isotro-pic (vertical permeability [kv] = horizontal per-meability [kh]), reducing with depth parallel tothat of the surrounding class 2 sediments. In sim-ulations of fracture baffles, the fracture zone has10% porosity and a permeability 1.0 or 0.1 timesthe vertical permeability of the platform sediments(equivalent to a fracture kh 103–104 times lowerthan that of the sediments). Open fractures are sim-ulated with 50% porosity and a permeability of 1.0or 10 times the horizontal permeability of the plat-form sediments (equivalent to a fracture kv 10

3–104

times higher than that of the sediments). Theserepresent average property values for fracture zonecells, which contain a set of partially connectedfractures separated by matrix blocks. Additionalsimulations (results not shown) explore the impactof varying the vertical extent of the fracture zoneand comparing a blind fracture zone with one thatbreaks the platform top. The reactive surface area inthe fracture zone is equal to that of the sedimentsbecause these simulations focus solely on the effectof the fracture zones on flow and hence reactionsin the bulk of the platform instead of modeling dia-genetic processes within the fracture zone.


Reducing horizontal permeability in the frac-ture zone significantly decreases both total fluidflux and the proportion of this that penetratesthe platform interior, and reduces advective cool-ing (Figure 12, left columns). Because of the re-duction in flow, and despite the warmer platform,less of the platform is dolomitized compared withthe baseline simulation. With a fracture zone per-meability equal to the vertical permeability of theplatform sediments, at 15 m.y., complete dolomiti-zation is limited to within 2–3 km (1.2–1.8 mi) ofthe margin, with a broader zone of partial dolomi-tization. With one order of magnitude lower frac-ture permeability, dolomitization is restricted tothe narrow area between the margin and the frac-ture zone. The enhanced dolomitization potentialof the rather warmer interior cannot be realized be-cause of the limited fluid flux. In both simulations,the effect of focusing of flow at the base of the frac-ture zone is evident. Although the position of theresulting dolomite zone is an artifact of the partic-ular permeability distribution specified, a zone ofenhanced dolomitization will likely occur wherea comparable permeability structure leads to fo-cusing of flow.

A fracture zonewith enhanced vertical perme-ability significantly increases fluid flow butmost ofthis flow is pirated by the fracture zone (Figure 12,right columns), and as for the lower permeabilityfracture zone, fluid flow into the interior is re-duced. Advective cooling is less than the baselinesimulation, although as horizontal permeability ismaintained within the fracture zone, not to theextent seen in the low-permeability fracture zonesimulations. After 15 m.y., the dolomite body isnot dissimilar in shape to the baseline, but the lat-eral extent is reduced; the completely dolomitizedzone extending not 15 km (9 mi) from the marginbut only 10 and 3 km (6 and 1.8 mi) for fracturepermeabilities, respectively, 1 and 10 times thehorizontal permeability of the sediments.

The presence of a fracture zone, whether as aconduit or baffle to flow, reduces dolomitization inthe main part of the platform. Simulations (notshown) with a fracture zone extending to shallowerdepth (1000 m [3290 ft]) indicate that the focus-ing of flow beneath the fracture zone (as shown

in Figure 12) leads to the development by 15 m.y.of a dolomite body extending some 10 km (6 mi)into the platform interior.Where the fracture zoneis blind, extending from 500- to 1500-m (1640- to4930-ft) depth, flow in the upper 500 m (1640 ft)of the platform is mostly unfettered and sufficientto generate a dolomite distribution not signifi-cantly different from the baseline simulation.

DISCUSSION

Our RTM simulations suggest that geothermalconvection can drive pervasive massive replace-ment dolomitization in isolated carbonate plat-forms over a 10–30-m.y. time scale. Because ofcomplex nonlinear coupling between fluid flowand reactions, the very slow rates of dolomitiza-tion previously estimated by Wilson et al. (2001)from short-term (<0.1 m.y.) simulations signifi-cantly underestimated the potential of this pro-cess. Simulations produce neither the sharp reac-tion fronts, which typify hydrothermal dolomites(Davies and Smith, 2006), nor the diffuse reduc-tion in dolomite abundance from fluid source alongthe fluid-flow path seen in some reflux dolomites(Saller and Henderson 1998; Jones and Xiao,2006). Instead, dolomite forms most rapidly with-in the upper 500 m (1640 ft) of the platform in azone extending up to 10 km (6 mi) from the plat-form margin, which is at the leading edge of abroad zone of rather slower dolomitization. Overtime, this forms a wedge-shaped dolomite body,which thins from the platform margin to the inte-rior. Dolomitization releases calcium into solu-tion, resulting in precipitation of anhydrite cementdownstream of the dolomitization zone wheretemperatures exceed 50°C. This zone of anhydriteis spatially separate from the contemporaneousdolomite, occurring at great depth (1–2 km [0.6–1.2 mi]) and in the platform interior.

Our simulations suggest that much of the geo-thermal dolomite forms at temperatures of 20–30°C. This corresponds well with some fieldstudies of seawater dolomites that have invokedgeothermal convection (e.g., Saller, 1984; Hendryet al., 2002; Whitaker et al., 2004). However,

many studies that invoke a normal seawater originfor early dolomites have not recognized the po-tential function of geothermal convection to formrelatively low-temperate dolomites. Others, in-cluding Machel (2004) and Wright and Wacey(2004), have called upon geothermal convectionto explain seawater dolomites at intermediateburial depths at higher (50–70°C) temperatures,comparable to those suggested by the earlier RTMstudies of Wilson et al. (2001). In such cases, earlynonideal dolomites (Nordeng and Sibley, 1994)formed at relatively cool temperatures may haverecrystalized during burial (Gregg, 2004) and thusrecord the temperature of recrystalization insteadof original formation.

The model predicts mole-for-mole replace-ment of calcite by dolomite, leading to an increasein porosity, permeability, and thus in dolomitiza-tion rate as the reaction progresses. In contrast toRTM simulations of dolomitization by refluxingbrines (Jones and Xiao, 2006), only very minoramounts of carbonate are contributed from sea-water, and no significant volumes of dolomite ce-ment precipitate (overdolomitization). This is be-cause the relative rates of calcite dissolution anddolomite precipitation and thus the evolution ofporosity are controlled by the fluid flux and geo-chemistry (Machel, 2004). It is thus likely that,where porosity has remained unaltered or is re-duced by dolomitization (Lucia, 2004), sourcefluids are modified seawater.

Feedbacks between porosity, permeability, anddolomitization are dependent upon the porosity-permeability transform employed (here a simpli-fied Kozeny-Carmen equation that is independentof mineralogy). Some dolomites exhibit a clearpositive relationship between porosity and perme-ability as a function of crystal size and connectivitybetweenpores (Luoet al., 1994;Gregg, 2004).How-ever, as Ehrenberg demonstrated for dolomites oftheMioceneMarion Plateau (2004) and elsewhere(Ehrenberg et al., 2006), porosity-permeabilityvalues do cluster along a single trend that approx-imates the Kozeny-Carmen curve despite a widetextural diversity. TheMarionPlateaudolomites ap-pear to have formed from normal or slightly mod-ified seawater in a continental margin setting and


increase in abundance seaward in amanner directlycomparable to our geothermal dolomitization simu-lations. Thus, although not fully representing thecomplexities in sediment texture and pore charac-teristics, which result fromdolomitization and con-trol reactions, themodel used here provides amean-ingful first approximation.

Our baseline packstone-wackestone platformis a laterally extensive (half of a symmetrical 50-km[31-mi]-wide platform) thick (300m [9870 ft]) car-bonate sequence with high relief (2000-m [6580-ft]deep ocean basin), which remains undolomitizedin the platform interior and at depth after 15–30 m.y. Simulations of narrower and shallowerplatforms indicate not only that geothermal dolo-mitization does not require such a large platform,but also that a greater proportion of the smallerplatforms is dolomitized. However, in these coolerplatforms, no significant predicted anhydrite ce-mentation is observed. This may explain the ab-sence of anhydrite cementation in low-relief plat-forms such as the Marion Plateau (Ehrenberg,2004), whereas such cements have been reportedfor higher relief platforms such as Karachagnak(Hendry et al., 2002). Dolomitization requires anelevated geothermal heat flux, although increas-ing the value relative to the baseline (passive mar-gin) value enhances rates of both dolomitizationand anhydrite cementation.

Given the apparent efficacy of geothermal con-vection, these RTM simulations lead us to questionwhy all carbonate platforms are not dolomitized.Sensitivity analyses identify two important sets ofcontrols on geothermal dolomitization. First, geo-thermal convection will be significantly less effec-tive in dolomitizing circular platforms such as iso-lated atolls than linear platforms with an aspectratio greater than 4:1 (length:width) typical of at-tached platforms. Second, specification of realisticinitial sediment properties (in particular perme-ability and reactive surface area) is critical formean-ingful prediction of dolomitization. Grainy plat-forms, which experience very active geothermalconvection and consequently significant cooling,remain mostly undolomitized because of the lowerreactive surface area of the larger grains. Similarly,the low permeability of muddy platforms restricts


fluid flow and thus dolomitization to the very mar-gin of the platform despite the high reactive surfacearea of the sediments. In these generic simulationsof homogenous (but anisotropic) platforms, onlywhere neither permeability nor reactive surfacearea is limiting can significant geothermal dolomi-tization occur. Furthermore, introducing a singlenarrow vertical band of contrasting permeabilityat the platform margin significantly reduces dolo-mitization of the platform interior, independentof whether this provides a vertical flow conduitor a baffle to flow.

Simple representations of layered and frac-tured platforms show complex interactions be-tween flow units and diagenetic behavior despitecapturing only a fraction of the depositional and dia-genetic heterogeneity of real platform carbonates.Deterministic simulations can explicitly incorpo-rate fine-scale spatial variability in initial properties,but parameterization of suchmodels is challengingdue to the lack of distributed initial condition data.Complex models can be populated stochastically(Jones and Xiao, 2005; Xiao and Jones, 2007),from proxies such as geophysical data (Chen et al.,2004) or from forward sediment models. In highlyheterogeneous systems, fluid flow tends to be chan-neled through themore permeable routes, bypassingmuch of thematrix within which reaction rates arereduced (Steefel et al., 1998;Harvey andGorelick,2000). Model cells can be partitioned into fractureand matrix (the dual-porosity approach; Warrenand Root, 1963) or matrix blocks subgridded ac-cording to distance from the fracture (themultipleinteracting continua of Pruess and Narasimhan,1985). Meaningful simulations of real platformsdepend on an accurate representation of key hydro-stratigraphic details such as confining beds, faults,and fractures. Advances in both computing powerand numerical algorithms are improving our abilityto represent important hydrostratigraphic detailssuch as thin confining layers and faults. Suchmod-els have been used to explicitly simulate diage-netic alteration zones developed along fractures,coupling progresses operating within the fractureand the matrix (e.g., Matthäi et al., 2004), and of-fer considerable potential for modeling carbonatediagenesis.

Finally, although linear platformsmay bemoresusceptible to geothermal dolomitization, suchplatforms are commonly developed along conti-nental margins. For attached platforms, the dis-charge of meteoric waters from the hinterland(not simulated here) may also have an importantimpact on both fluid flow and reactions. Model-ing of fluid flow in the partially emergent Floridaplatform by Hughes et al. (2007) illustrates thecomplex interaction between meteoric and geo-thermal flow systems, independent of any diage-netic effects. Whereas submixing zone flow of sea-water may enhance geothermal dolomitizationduring periods of platform top exposure, refluxof evaporitic brines can reduce or eliminate geo-thermal convection (Jones et al., 2004) and drivemore rapid dolomitization and precipitation ofdolomite and anhydrite cements (Jones and Xiao,2005; Al-Helal et al., 2009). In addition to eustaticchanges in relative sea level, sediments will sub-side though zones of more or less rapid reaction,with accumulation of fresh undolomitized sedi-ment to fill accommodation. Although insignifi-cant in passivemargin settings, thermal and flexuresubsidence can amount to as much as 400–500 m(1320–1640 ft) over 15 m.y. (using rates fromAngevine et al., 1990).

For platforms where rates of geothermal dolo-mitization are slow compared to the rate at whichrelative sea level changes, these models may fail tocapture important elements in the diagenetic sys-tem. At present, no models explicitly couple reac-tive transport with evolving boundary conditionsand platform geometry. One approach is to modelthe stepwise evolution of sedimentary sequencesat coarse temporal resolution, as exemplified byrecent RTM simulations of dolomitization of theNisku reefs, Western Canada sedimentary basin(Jones et al., 2009). However, simpler rule-baseddiagenetic schemes coupled to forward sedimentmodels, which simulate the evolution of platformarchitecture and facies geometry, enable these feed-backs to be evaluated (Whitaker et al., 1997, 1999;Paterson et al., 2008). Although generic simula-tions such as those presented here can providenew insights into specific processes, modeling thecomplex interactions between different hydro-

chemical systems over time represents an impor-tant direction for future research.

CONCLUSION

Numerical RTM simulations are a powerful com-plementary tool that can improve our understand-ing of the complex nonlinear coupling betweenphysical and chemical processes controlling dolo-mitization and associated diagenetic processes oc-curring over long spans of time and/or at greatdepth. Simulations presented in this study haveprovided new insights into five specific questions.

1. Geothermal convection of normal seawater canform a large body of 100% dolomite within thetime scale of millions to a few tens of millions ofyears and is accompanied by precipitation ofanhydrite cements downstream of the dolomitebody but only very minor dolomite cements.The rate of geothermal dolomitization and thesize of the dolomite body formed have previ-ously been significantly underestimated dueto nonlinearities in the rate of dolomitization(which accelerates as the abundance of dolo-mite increases).

2. The dolomite body is characteristically thicker atthe platform margin and at shallow depth, thinstoward the platform interior, and forms at tem-peratures that are cooler than previously sug-gested, mostly in the range of 20–40°C.

3. Geothermal dolomitization is mostly indepen-dent of platform thicknesses and width but isless effective in circular than in elongate plat-forms. Changing boundary conditions, includingplatform top exposure and platform drowning,and changing basal heat flux have a relativelymoderate effect on dolomitization rate and/ordolomite body geometry.

4. Dolomitization is critically sensitive to sedi-ment permeability and the reactive surface area,which are commonly inversely related. The re-stricted fluid flux through low-permeabilitymuddy platforms limits geothermal dolomitiza-tion to the platformmargin. The rate of dolomi-tization of the permeable grainy platforms is


also lower, limited by the reactive surface area,and occurs only in the platform core due towide-spread cooling of the platform.

5. Vertical layering of sediment types produces acomplex vertical diagenetic stratigraphy, favor-ing more reactive beds at shallow depth wherepermeability is not limiting but switching tomore permeable beds at depth. The presenceof a bank-marginal zone of fracturing limits do-lomitization of the platform interior, irrespec-tive of whether the fractures are open or sealed.

Modeling allows us to identify important fea-tures of carbonate platform sedimentology and ar-chitecture and couplings between the constitutiveprocesses. This enables prediction of the behaviorof similar systems from sparse observations, andsimplification of geological complexity with mini-mum loss of physical realism. The RTM resultsprovide a process-based framework for understand-ing the evolution of dolomite, associated anhydritecements, and petrophysical properties. Insights fromthese simulations can be applied to reservoir char-acterization to help constrain and develop scenar-ios for subsurface correlations of dolomite bodiesand their connectivity and producibility. Themod-eling results, calibrated with well-based observa-tions, have the potential to generate predictive dia-genetic rules that can be used to guide estimation ofporosity and permeability distribution in reservoirmodels. Challenges to improving our RTM simula-tions of dolomitization arise from uncertainties inphysical and chemical parameters (especially per-meability and the reactive surface area), uncertain-ties in dolomitization kinetics at low temperatures,appropriate representation of such inherently het-erogeneous systems, and the nonstationarity ofboundary conditions over such long times.

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