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Experimental kinetic study of organic matter maturation: Time and pressure effects on vitrinite reflectance at 400 °C Ronan Le Bayon a,, Gerhard P. Brey b , W.G. Ernst c , Rafael Ferreiro Mählmann a a Institut für Geowissenschaften, Technische Universität Darmstadt, Schnittspahnstrasse 9, D-64287 Darmstadt, Germany b Institut für Geowissenschaften, Abt. Petrologie und Geochemie, J.W. Goethe-Universität, Altenhöferallee 1, D-60438 Frankfurt am Main, Germany c Department of Geological and Environmental Sciences, Stanford University, Stanford, CA 94305-2115, USA article info Article history: Received 6 July 2010 Received in revised form 26 January 2011 Accepted 28 January 2011 Available online 3 February 2011 abstract We carried out a laboratory rate study to elucidate and quantify the effects of time and pressure on vitr- inite reflectance (VR). A series of confined system maturation experiments was conducted at 400 °C and at pressures of 2, 10 and 20 kbar. Experiments were performed on dry (no water added) xylite of swamp cypress and involved run lengths from 0 s to 25 days. At 400 °C, our experimental results demonstrate pressure and heating time to be important variables that promote VR increase and therefore the maturation of Type III organic material. VR increases with time at each investigated pressure. Despite rapid initial kinetics, the increase in VR decelerates with time at each pressure. When VR < 1.44%, increasing pressure reduces the rate of VR increase and hence retards the initial VR enhancement with time. The retarding effect of pressure on VR increase diminishes with enhancing VR. The retardation of VR increase is insignificant for geological maturation at 400 °C because a VR of 1.44% is attained in only a few hours. When VR > 1.44%, increasing pressure counteracts the deceleration of VR increase with time and thus greatly enhances the increase in VR with time. Evidently, vitrinite maturation takes place rapidly in a dry confined system and does not require addition of water to occur. The strong effect of the experimental heat-up on VR is obvious even for very short experiments and must be corrected in kinetic analysis. The evolution of VR with heating time (t) and pressure (P) at 400 °C from an initial VR of 0% is well described by our new power law rate equation VRðP; 400 C;tÞ¼ðkðP; 400 CÞtÞ nðP;400 CÞ ; where the exponent n(P, 400 °C) and the rate constant k(P, 400 °C) increase with pressure. We regard this kinetic formulation as a step toward a general equation describing VR evolution as a function of time, pres- sure and temperature for Type III organic matter. The potential of the power law formalism to model VR from any starting VR and for complex metamorphic and heating time histories is shown by making explicit directions on how to use such a kinetic equation. Ó 2011 Elsevier Ltd. All rights reserved. 1. Introduction Metamorphic organic petrology aims to identify, understand and quantify processes and factors responsible for the formation and transformation of organic geomaterials and their associated physical and chemical properties. In particular, it is devoted to the study of metamorphism and maturation in low to very low temperature metamorphic terranes. There are many reasons for this, but all are ultimately related to hydrocarbon exploration and a fuller understanding of the Earth’s geodynamic evolution. It is very difficult to carry out metamorphic studies in terranes con- sisting mostly of low temperature metasedimentary rocks because such conditions lead to sluggish reactions. However, the presence of vitrinite phytoclasts provide an opportunity to understand metamorphic and geodynamic evolution by determining rock pressure–temperature (PT) conditions and the degree of maturity with respect to hydrocarbon generation. This stems from the recognition that vitrinite reflectance (VR) measurements monitor the maturation of organic material because VR in host rocks is demonstrated to be correlated with coal rank (e.g., van Krevelen, 1953; Teichmüller and Teichmüller, 1954; Lopatin, 1971; Hood et al., 1975; Hunt, 1979; Robert, 1980; Tissot and Welte, 1984; Roksandic, 1986). Consequently, tremendous progress has been made toward better understanding of vitrinite maturation and reflectance over the past 50 years. However, clarification of the physical and chemical parameters that control vitrinite reflectance is necessary because VR provides valuable and even unique aid for hydrocarbon exploration and insight into geodynamic evolution of 0146-6380/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.orggeochem.2011.01.011 Corresponding author. Tel.: +49 (0)61 51 16 65 41; fax: +49 (0)61 51 16 40 21. E-mail address: [email protected] (R. Le Bayon). Organic Geochemistry 42 (2011) 340–355 Contents lists available at ScienceDirect Organic Geochemistry journal homepage: www.elsevier.com/locate/orggeochem
Transcript
Page 1: LeBayon 2011 Organic-Geochemistry

Organic Geochemistry 42 (2011) 340–355

Contents lists available at ScienceDirect

Organic Geochemistry

journal homepage: www.elsevier .com/locate /orggeochem

Experimental kinetic study of organic matter maturation: Time and pressureeffects on vitrinite reflectance at 400 �C

Ronan Le Bayon a,⇑, Gerhard P. Brey b, W.G. Ernst c, Rafael Ferreiro Mählmann a

a Institut für Geowissenschaften, Technische Universität Darmstadt, Schnittspahnstrasse 9, D-64287 Darmstadt, Germanyb Institut für Geowissenschaften, Abt. Petrologie und Geochemie, J.W. Goethe-Universität, Altenhöferallee 1, D-60438 Frankfurt am Main, Germanyc Department of Geological and Environmental Sciences, Stanford University, Stanford, CA 94305-2115, USA

a r t i c l e i n f o a b s t r a c t

Article history:Received 6 July 2010Received in revised form 26 January 2011Accepted 28 January 2011Available online 3 February 2011

0146-6380/$ - see front matter � 2011 Elsevier Ltd. Adoi:10.1016/j.orggeochem.2011.01.011

⇑ Corresponding author. Tel.: +49 (0)61 51 16 65 41E-mail address: [email protected] (R.

We carried out a laboratory rate study to elucidate and quantify the effects of time and pressure on vitr-inite reflectance (VR). A series of confined system maturation experiments was conducted at 400 �C andat pressures of 2, 10 and 20 kbar. Experiments were performed on dry (no water added) xylite of swampcypress and involved run lengths from 0 s to 25 days.

At 400 �C, our experimental results demonstrate pressure and heating time to be important variablesthat promote VR increase and therefore the maturation of Type III organic material. VR increases withtime at each investigated pressure. Despite rapid initial kinetics, the increase in VR decelerates with timeat each pressure. When VR < 1.44%, increasing pressure reduces the rate of VR increase and hence retardsthe initial VR enhancement with time. The retarding effect of pressure on VR increase diminishes withenhancing VR. The retardation of VR increase is insignificant for geological maturation at 400 �C becausea VR of 1.44% is attained in only a few hours. When VR > 1.44%, increasing pressure counteracts thedeceleration of VR increase with time and thus greatly enhances the increase in VR with time. Evidently,vitrinite maturation takes place rapidly in a dry confined system and does not require addition of water tooccur. The strong effect of the experimental heat-up on VR is obvious even for very short experiments andmust be corrected in kinetic analysis. The evolution of VR with heating time (t) and pressure (P) at 400 �Cfrom an initial VR of 0% is well described by our new power law rate equation

VRðP;400 �C;tÞ ¼ ðkðP;400 �CÞtÞnðP;400 �CÞ;

where the exponent n(P, 400 �C) and the rate constant k(P, 400 �C) increase with pressure. We regard thiskinetic formulation as a step toward a general equation describing VR evolution as a function of time, pres-sure and temperature for Type III organic matter. The potential of the power law formalism to model VRfrom any starting VR and for complex metamorphic and heating time histories is shown by making explicitdirections on how to use such a kinetic equation.

� 2011 Elsevier Ltd. All rights reserved.

1. Introduction

Metamorphic organic petrology aims to identify, understandand quantify processes and factors responsible for the formationand transformation of organic geomaterials and their associatedphysical and chemical properties. In particular, it is devoted tothe study of metamorphism and maturation in low to very lowtemperature metamorphic terranes. There are many reasons forthis, but all are ultimately related to hydrocarbon explorationand a fuller understanding of the Earth’s geodynamic evolution.It is very difficult to carry out metamorphic studies in terranes con-sisting mostly of low temperature metasedimentary rocks because

ll rights reserved.

; fax: +49 (0)61 51 16 40 21.Le Bayon).

such conditions lead to sluggish reactions. However, the presenceof vitrinite phytoclasts provide an opportunity to understandmetamorphic and geodynamic evolution by determining rockpressure–temperature (P–T) conditions and the degree of maturitywith respect to hydrocarbon generation. This stems from therecognition that vitrinite reflectance (VR) measurements monitorthe maturation of organic material because VR in host rocks isdemonstrated to be correlated with coal rank (e.g., van Krevelen,1953; Teichmüller and Teichmüller, 1954; Lopatin, 1971; Hoodet al., 1975; Hunt, 1979; Robert, 1980; Tissot and Welte, 1984;Roksandic, 1986). Consequently, tremendous progress has beenmade toward better understanding of vitrinite maturation andreflectance over the past 50 years. However, clarification of thephysical and chemical parameters that control vitrinite reflectanceis necessary because VR provides valuable and even unique aid forhydrocarbon exploration and insight into geodynamic evolution of

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R. Le Bayon et al. / Organic Geochemistry 42 (2011) 340–355 341

low temperature metamorphic terranes. Measurement of vitrinitereflectance using a microscope equipped with a photometer issimple and practical. Vitrinite reflectance can be measured onphytoclasts of a few micrometers in diameter in host rocks orexperimental samples.

Several variables influencing vitrinite reflectance are alreadyrecognized and have been quantitatively estimated by experi-ments. Others are poorly understood.

For decades, it has been well established that temperature is amajor factor controlling vitrinite reflectance (Lopatin, 1971; Tissotand Espitalié, 1975; Waples, 1980; Tissot et al., 1987; Burnham andSweeney, 1989; Suzuki et al., 1993; Huang, 1996; Dalla Torre et al.,1997; Ernst and Ferreiro Mählmann, 2004). Because organic mattermaturation is irreversible, VR only records the maximum tempera-ture to which the enclosing rocks were exposed. Measurement ofvitrinite reflectance is therefore a fundamental tool widely usedby earth scientists and oil, gas and coal industry technologists toestimate paleotemperature in low grade metamorphic settings(e.g., Frey et al., 1980; Kisch, 1987; Underwood et al., 1999;Ferreiro Mählmann, 2001; Árkai et al., 2002; Frings et al., 2004)as well as the thermal maturity of hydrocarbon source rocks(e.g., Durand and Espitalié, 1976; Tissot et al., 1987; Johnssonet al., 1993; Armstrong et al., 1996; Parris et al., 2003).

The roles of starting material composition, oxygen fugacity andwater content have been subject to experiments (Huang, 1996;Ernst and Ferreiro Mählmann, 2004). Humite impregnated withliptinite (e.g., resinite, bituminite, exsudatinite from alginite)shows reduced VR (Huang, 1996; Ernst and Ferreiro Mählmann,2004). These experimental studies confirm the retarding/suppress-ing effect of hydrogen rich macerals on VR reported from naturalenvironments by Wolf (1978), Hutton and Cook (1980), Price andBarker (1985), Wenger and Baker (1987), Raymond and Murchison(1991), Petersen and Rosenberg (1998) and Carr (2000). Ernst andFerreiro Mählmann (2004) experimentally found that oxygenfugacity does not affect the rate of vitrinite maturation. Other fac-tors such as fluid flow, the presence of oil and the partial pressuresof CO2, CH4 and argon were experimentally shown by Huang(1996) to have imperceptible influence on the kinetics of vitrinitereflectance evolution. In an effort to evaluate the role of water inVR evolution, Huang (1996) conducted a series of lignite matura-tion experiments in a hydrous (sea water added) confined system,an anhydrous (no water added) confined system and an anhydroussystem (no water added) open to argon gas. Despite a limited num-ber of anhydrous confined experiments, this study concluded thatVR increases in confined systems at similar rates with or withoutadded water. In contrast, it also demonstrated that VR evolutionis retarded in an open system compared to a confined system. Thisis in accord with experimental results of Landais et al. (1994),which showed that confined and hydrous pyrolysis experimentson Type III coal yield similar VR values. Furthermore, Monthiouxet al. (1985) concluded from their chemical studies on Type III or-ganic matter that confinement of generated gas in anhydrousexperiments produces results similar to those in hydrous experi-ments. This led Monthioux et al. (1985) to postulate that the pres-ence of water is not necessary when pyrolysis is performed in aconfined system. Consequently, Huang (1996) suggested thatwater and/or other pyrolysis products generated during the earlystage of organic matter pyrolysis in anhydrous confined systemsallow VR to change at rates similar to that under hydrous confinedconditions. Nevertheless, the need for a hydrous (a water-excesssystem) maturation to promote VR requires clarification becausea series of dry (no water added) confined experiments to simulatevitrinite maturation has never been carried out at fixed P–Tconditions on Type III organic matter. Thus, we investigate thematuration of Type III organic matter in dry (no water added)systems in this study. This will confirm whether the maturation

of Type III organic matter occurs in dry systems. This result willbe compared to a series of hydrous (water added) confined matu-rations in a further communication in order to identify whetheradded water has an effect on VR.

While the effect of temperature on vitrinite reflectance has beenwell constrained, the influence of time remains controversial. Onthe one hand, it has been argued (e.g., Price, 1983; Ritter, 1984;Barker, 1989, 1991) that vitrinite reflectance evolution is stabilizedrapidly at geological timescales – within only 10 years. On theother hand, both the effective heating time and temperature havebeen recognized as important (Lopatin, 1971; Hood et al., 1975;Waples, 1980; Burnham and Sweeney, 1989; Sweeney andBurnham, 1990; Hunt et al., 1991; Waples et al., 1992). These earlystudies were supported by recent experiments (Huang, 1996; DallaTorre et al., 1997; Ernst and Ferreiro Mählmann, 2004) showingthat, whereas time is important, the major variable that deter-mines VR over geological time intervals is host rock temperature.Based on these assumptions, several field and experimentally cal-ibrated models using Arrhenius kinetics were developed to predictthe evolution of vitrinite reflectance (Waples, 1980; Burnham andSweeney, 1989; Larter, 1989; Suzuki et al., 1993; Huang, 1996;Dalla Torre et al., 1997; Ernst and Ferreiro Mählmann, 2004). How-ever, improved understanding of the effect of time on vitrinitereflectance is still needed.

Although considerable efforts have been directed towardunderstanding and quantifying the effect of temperature, oxygenfugacity and starting material upon VR evolution, the effect of pres-sure on Type III organic matter maturation remains largely un-known. Despite the probable importance of pressure on VRevolution, all of our information comes either from limited exper-iments with inconsistent results (Chandra, 1965; Hryckowianet al., 1967; Goodarzi, 1985; Mastalerz et al., 1993; Hill et al.,1994) or from controversial estimates from field studies. Estimatesbased on paleometamorphic conditions are poorly constrained invitrinite bearing terranes and their surrounding silico-calcic rocks(e.g., Bostick, 1974; Diessel et al., 1978; Kisch, 1987; Dalla Torreet al., 1994, 1996). Conflicting observations in sedimentary basinsdocument both enhanced (Law et al., 1989; Hunt, 1996) and re-tarded (McTavish, 1978; Hao et al., 1995, 2007) VR profiles withthe onset of overpressure (for a recent review, see Carr (2000)and references therein). In general, pressure has been widely re-garded as having little influence on the maturation of Type III or-ganic matter, at least when compared to temperature andheating time (e.g., Teichmüller and Teichmüller, 1979; Stachet al., 1982; Murchison et al., 1985; Huang, 1996; Ernst and Ferre-iro Mählmann, 2004). In summary, considerable confusion existsabout the pressure effect on vitrinite maturation. The lack of clear,reliable information on the influence of pressure on VR is surpris-ing if one considers the strong pressure dependence of the wellknown graphitization process from experimental studies (e.g., Bon-ijoly et al., 1982) and the importance of pressure as metamorphicagent in most geological settings. Knowledge and accurate deter-mination of the pressure effect on VR evolution kinetics is neededto gain insight into and quantify the diverse processes that span or-ganic metamorphic petrology. Thus, it is essential to experimen-tally investigate the influence of pressure on VR evolution rates.

In addition to pressure, the effect of experimental heat-up toreach the desired run temperature on the material during artificialmaturation is still unknown. The experimental heat-up is the rapidincrease in run temperature from room temperature to the desiredfinal run temperature (i.e., 400 �C). To date, most of the existingexperimental studies on maturation of organic material do notconsider the possible influences of experimental heat-up on vitri-nite reflectance (e.g., Huang, 1996; Ernst and Ferreiro Mählmann,2004). Dalla Torre et al. (1997) state that experimental heat-uphas no effect on VR as long as the final temperature is reached in

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<30 min. This is in contrast with the kinetic study of Huang (1996),which predicts that VR strongly changes between 300 and 400 �Cwith run duration as short as 15 min. A stringent experimentalevaluation of heat-up effect on vitrinite maturation is needed.

Our main goal in this work is to elucidate and quantify the ef-fects of time and pressure on vitrinite reflectance in dry (no wateradded) systems. Furthermore, this experimental study aims to as-sess the effects of dry maturation and experimental heat-up to thefinal temperature on VR. The research consists of a series of matu-ration experiments on organic matter at 400 �C in a dry, confinedsystem at 2, 10 and 20 kbar for various run times. A kinetic analysisof the experimental results was carried out to quantify and under-stand the evolution of measured vitrinite reflectance as a functionof heating time and pressure. We formulated a pressure-dependentempirical rate equation for the evolution of vitrinite reflectance at400 �C and evaluated the pressure dependence of the rate lawparameters to fully assess the effect of pressure on the kinetics ofVR evolution. We provide explicit directions on how to use thepower law formalism to model VR for any starting VR and complexmetamorphic and heating time histories.

It is of special interest to formulate such a VR rate equation be-cause it provides a step toward a general equation that describesVR evolution as a function of time, pressure and temperature.The advantage of this VR rate equation is that it does not requirecomplete understanding of the complex chemical reactions thatregulate vitrinite maturation. This general empirical kinetic equa-tion will be elaborated in a future report. This VR rate equation willbe a useful tool to model the VR–T–t conditions in vitrinite bearingsedimentary basins and to estimate the P–T–t conditions in vitri-nite bearing metamorphic terranes occurring in various tectonicsettings (e.g., exhumed subducted terranes, collided terranes inorogenic wedges). This will aid to gain insight into geodynamicevolution of sedimentary and metamorphic terranes. Moreover,this future general empirical kinetic equation will help to improvehydrocarbon generation modeling in sedimentary basins.

Fig. 1. Photograph (a) and photomicrograph (b) (reflected light) of the startingmaterial that consists of swamp cypress (Taxodioidea taxodium). The cellularmicrostructure displays the cell walls consisting of telinite that surround theinfilling of the cell lumens. This xylite sample is Middle Eocene in age.

2. Experimental and analytical procedures

2.1. Experimental philosophy

We conducted an isothermal laboratory rate study of Type IIIorganic material maturation at various pressures to understandand quantify the effects of time and pressure on vitrinite reflec-tance. This series of maturation experiments was performed at400 �C in a confined system on dry (no water added) xylite ofswamp cypress at pressures of 2, 10 and 20 kbar. Experiments in-volved run lengths from 0 s to 25 days and were carried out byemploying a high pressure piston-cylinder apparatus and cold-sealpressure vessels. We chose 400 �C for our experiments to avoidsluggish reactions leading to difficulties in measuring maturationrates. Nevertheless, experiments at lower and higher temperaturesin dry and wet (water added) systems are under way and will bethe subject of a future report.

2.2. Starting material

We used a xylite of swamp cypress (Taxodioidea taxodium)(Fig. 1a) as starting material for the experiments because it is thearchetype of the botanical and chemical precursor of the humi-nite/vitrinite group macerals. The xylite sample is Middle Eocenein age and was collected in the Helmstedt open pit mine from coalseam 6 of the Wulfersdorf group, in the eastern Helmstedt syn-cline, Braunschweig mining area, northern Germany (Lenz and Rie-gel, 2001). The Wulfersdorf seam group represents a coastalswamp paleoecosystem. Swamp cypresses are poorly represented

in the swamp forests and hummocks of the Wulfersdorf paleoeco-system and only rare stems and branches are found (Lenz and Rie-gel, 2001). The sample was stored at ambient conditions anduntreated before the experiments.

The xylite sample displays a recognizable cellular microstruc-ture (Fig. 1b) in which cell walls consisting of telinite surroundstructureless infillings of the cell lumens. The xylite sample lacksliptinite macerals, such as resinite, sporopollenite, chlorophyllinite,cutinite and bituminite that are known to suppress vitrinite reflec-tance due to their high hydrogen content (for a recent review, seeCarr (2000) and references therein). Ernst and Ferreiro Mählmann(2004) recently confirmed vitrinite reflectance suppression inhuminite by bituminite and resinite impregnation in their experi-mental study. In addition, the Wulfersdorf swamp cypress stemsshow no oxidation and are very poor in other hydrogen rich plantconstituents, such as resin, wax and tannin. Furthermore, no algalagglomerates occur in the sample bearing paleoecosystem. Thisobservation is important because algal agglomerates could sup-press vitrinite reflectance of the neighboring telinite due to theirhigh hydrogen contents (e.g., Stach et al., 1982; Carr, 2000).

We measured a low atomic H/C ratio of 1.27 ± 0.03 in the imma-ture xylite sample. This confirms the hydrogen poor nature of thestarting material. A vitrinite reflectance VR = 0.167 ± 0.020% wasmeasured in the starting material, indicating that the initial vitri-nite/organic matter was extremely immature prior to the experi-ments. This allows the investigation of the largest possible VR

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range because maturation prior to the experiment does not inter-fere with our results. This xylite sample of swamp cypress is anideal botanical, chemical and physical (low VR) starting materialon which to perform artificial vitrinite maturation experiments.The botanical origin and low H/C ratio of the sample indicate TypeIII organic matter in the van Krevelen terminology. This type of or-ganic matter is a good natural gas source, but is less productive ofoil (e.g., Stach et al., 1982; Taylor et al., 1998).

2.3. Experimental methods

The use of a high pressure piston-cylinder apparatus and cold-seal pressure vessels to carry out the vitrinite maturation experi-ments is based on the findings of Lewan et al. (1979), Monthiouxet al. (1985), Monthioux (1988), Horsfield et al. (1989), Landaiset al. (1989), Lewan (1993) and Vandenbroucke et al. (1993) thatnatural maturation of organic matter can be reproduced by labora-tory experimentation only if conducted in confined systems (i.e., insealed gold or platinum capsules under external pressure, with orwithout water). These workers found that organic matter heatedunder fully confined laboratory conditions follows the same evolu-tion path of H/C versus O/C atomic ratios as the natural coalifica-tion. In contrast, open system (under vacuum or inert gas) andclosed system (in sealed glass tubes and with water) maturationstudies do not yield geochemical data compatible with naturalsystems.

2.3.1. High pressure piston-cylinder experimentsExperiments at pressures of 10 and 20 kbar with temperature of

400 �C were conducted using the end loaded high pressure piston-cylinder apparatus of the Institut für Geowissenschaften, Abt.Petrologie und Geochemie, J.W. Goethe-Universität, Frankfurt amMain, Germany. We used Pt capsules and NaCl pressure-mediumassemblies (Fig. 2) in a 12.7 mm diameter piston-cylinder pressurevessel. The capsules consisted of a cylinder and two lids manufac-tured from platinum tubes and sheets. The Pt lids were fabricatedby folding the rims of the Pt disks (3.6 mm diameter and 0.2 mmthickness) at 90� by stamping the disks in a steel die. A Pt lidwas electric arc welded into one end of a Pt tube (5–7 mm long,3.03 mm outer diameter and 0.2 mm wall thickness). The capsule

10 mm

Mullite thermocouple pipe

Pyrophyllite ring

BN ringCrushable alumina ring

Pt capsule

Graphite diskGraphite cylinder

Furnace

Upper NaCl sleeveLower NaCl sleeve

Pressuremedium

Steel plug

Pt70Rh30/Pt94Rh6 (type B)thermocouple

NaCl cylinder }}

Fig. 2. Cross-section of the piston-cylinder assembly.

body was then annealed, hydraulically pressed to obtain a flat bot-tomed capsule and cleaned prior to the introduction of the drystarting material. The swamp cypress xylite was gently disaggre-gated to coarse and fine particles (0.1–1.0 mm in length,�0.1 mm thick) in an agate mill prior to loading into the Pt cap-sules. No water was added to the capsule. The xylite was filledand pressed into the capsule almost to the rim. The depth to therim must be sufficient to house the second Pt lid. The rim of thecapsule was then crimped down over the rim of the inserted lidand hydraulically pressed to cold seal the capsule rather than toweld it. This avoids potential thermal alteration of the charge.The cold sealed capsule (�4–5 mm long after closure) was placedvertically in a NaCl assembly acting as sample holder and pressuremedium. NaCl was chosen as pressure medium because it has goodisotropic mechanical behavior at the experimental temperature of400 �C. We machined all NaCl components by hydraulically press-ing dried NaCl of 99.99% purity at a maximum of 8 kbar in steeldies to reach at least 95% of the density of crystalline NaCl. Eachassembly consisted of a NaCl outer cylinder, a graphite heaterand an upper and a lower inner NaCl sleeve (Fig. 2). The lower in-ner NaCl sleeve housed the run capsule and the upper sleevehoused the thermocouple. A cylindrical graphite resistance furnacewas used as heater. A graphite disk was added at the bottom of thelower NaCl sleeve and graphite cylinder to improve formation of areliable heating circuit through the cell. The sample assembly wasplaced in the tungsten carbide core of the pressure cell. The entireassembly and thermocouple plate were then added to the piston-cylinder apparatus. To control run temperature, a Pt70Rh30–Pt94Rh6

(type-B) thermocouple was inserted axially into the assembly andlocated at a distance of 0.6 ± 0.03 mm above the flat top of the Ptcapsule. Thermocouple wires were placed inside a two-bore mull-ite pipe to isolate them from electric contact with the thermocou-ple plate and sample assembly. Experiments were pressurized tothe desired run pressure at room temperature and then heated to400 �C at a rate of 50 �C/min. This led to a heat-up time of<8 min. Temperature ramp rate and temperature during the exper-iment were controlled automatically via a programmable EURO-THERM power controller. Temperature was held constant towithin ±1 �C during experiments. Temperatures reported in thisexperimental study are uncorrected for potential thermal gradi-ents in the capsule. Stated values are thought to be accurate to±1 �C. Pressure was kept constant for the duration of the experi-ment by manual adjustment if necessary. Pressure is consideredto be accurate to ±1 kbar. Run conditions were maintained for 0 sto 25 days. Experiments were quenched in <10 s by switching offthe power to the heater whilst maintaining quasi run pressure.Afterwards, pressure was decreased in �30 min.

2.3.2. Cold-seal pressure vessel experimentsSeveral unsuccessful attempts were made to perform experi-

ments at 2 kbar and 400 �C using the high pressure piston-cylinderapparatus: The run capsules exploded. To overcome this problem,an alternative experimental method was used for low pressureexperiments. Experiments at a fixed pressure of 2 kbar were con-ducted in cold-seal pressure vessels in the hydrothermal labora-tory of the Geological and Environmental Sciences Department ofStanford University, California. The xylite was loaded into gold cap-sules. Run capsules were placed in cone-in-cone cold-seal pressurevessels (Kerrick, 1987) connected to a water pressure reservoir, aHeise bourdon tube gauge and an air driven hydraulic pump. Priorto beginning this study, each autoclave and thermocouple assem-bly was temperature calibrated against the melting point of NaClat 1 atm. After pressurization of an experimental sample to 2 kbaraqueous fluid pressure, the vessel was placed in a nichrome woundresistance furnace and externally heated to the desired tempera-ture using an electronic proportional temperature regulator

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connected to a chromel–alumel sensing thermocouple. The sampletemperature was read from the EMF a run thermocouple insertedin an external well in the hot end of the autoclave. Heating andcooling times for experiments were �30 min. Pressure and tem-perature uncertainties were ±25 bar and ±2 �C in cold-seal pressurevessels. Run conditions were maintained for 0 s to 25 days.

2.4. Analytical methods

After the experiments, the capsules were recovered and cut dia-metrically in half for vitrinite reflectance analysis. The preparationof vitrinite mounts consisted of plucking numerous vitrinite parti-cles from the recovered samples, embedding them in epoxy resinand then polishing the mounts at room temperature using 3, 1and 0.5 lm diamond powder and felted wool for the last polishto avoid scratches that cause relief and shadows that change reflec-tance. The same procedure of preparation for vitrinite mounts wasapplied to the initial material prior to experiments. VR measure-ments were performed at the Institut für Geowissenschaften ofthe Technische Universität Darmstadt, Germany. Vitrinite reflec-tance was measured according to standard procedures (Stachet al., 1982). We measured the 546 nm wavelength monochro-matic light reflected from the vitrinite mount surface using a pho-tomultiplier coupled to a Leitz Orthoplan-photometer microscopecalibrated with a single standard. The microscope was equippedwith a 125� oil immersion objective coupled with a 10� ocular.A non-drying immersion oil with a refraction index ne = 1.518 (at23 �C and for 546 nm wavelength monochromatic light) was usedfor reflectance measurements. The VR measurement equipmentwas placed on a sturdy work bench to avoid vibration duringmeasurement. In addition, measurements were operated in dimlight at about 21 �C. Calibration was done according to standardprocedures detailed by Taylor et al. (1998). Standards used for cal-ibration (with corresponding reflectance R) were: Yttrium–alumin-ium–garnet (R = 0.880%), gadolinium–gallium–garnet (R = 1.719%)and cubic zirconia (R = 3.114%). The quality of calibration waschecked every two hours during measurements. To calculate theVR mean value of an experimental sample, we conducted aminimum of 100 VR measurements. For vitrinite reflectance below1.3%, measured VR is the mean random vitrinite reflectance. Forvitrinite reflectance above 1.3%, measured VR is the maximumvitrinite reflectance determined under polarized light. Vitrinitereflectance measurements were only carried out on telinite.

Fig. 3. Photomicrographs (reflected light) showing the textural relations in runproducts from experiments at 400 �C and at different effective heating time andpressure conditions. (a) 0 s–20 kbar (run RLB-e84), (b) 15 min–20 kbar (run RLB-e26), (c) 1 day–20 kbar (run RLB-e07), (d) 25 days–20 kbar (run RLB-e01), (e)15 min–10 kbar (run RLB-e22), (f) 1 day–10 kbar (run RLB-e27), (g) 25 days–10 kbar (run RLB-e44), (h) 1 h–02 kbar (run GE-V8). T = telinite (cell wall); CL = celllumen; GD = granular decomposition of the organic material.

3. Experimental results

3.1. Microscopic observations

Prior to discussion of the VR results, it is necessary to report afew observations concerning microscopic evolution of the xylitematured at 400 �C as a function of pressure and time to expandour limited knowledge of isothermal maturation of Type III organicmatter. Before the experiments, the initial xylite displayed the eas-ily recognizable cellular microstructure of swamp cypress: Bright(on a grey scale) cell walls consisting of telinite surrounding thedark infilling of the cell lumens (Fig. 1b). After the experiments,several critical aspects of the organic maturation were observedin the experimentally matured xylite.

In all 2 kbar experiments with heating times P1 h, we foundinhomogeneous strong granular disintegration of the material toa fine mosaic structure typical of coking (Fig. 3h). This decomposedmaterial was difficult to measure because the grains were smallerthan the aperture of the photo-multiplier. Similar observationsdocument such a coking effect at 2 kbar and 400 �C (Ernst andFerreiro Mählmann, 2004). Nevertheless, some rare matured xylite

particles or parts of them isolated in the coke were preserved fromgranular disintegration. Some initial cellular (telinite and cell infill-ing) microstructures of the cypress were recognized in these pre-served grains, where VR was carefully measured. In the 2 kbarruns with heating times <1 h, no disintegration/coking occurredand the original botanical structure was preserved.

In all 10 and 20 kbar experiments, the initial cellular micro-structure of the wood (cell walls and cell lumens) was recognizable(Fig. 3a–g). There was no general gelification and therefore the cellwalls consisting of telinite were readily distinguished from the

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R. Le Bayon et al. / Organic Geochemistry 42 (2011) 340–355 345

infilling of the cell lumens. This distinction was straightforward inall experiments at 10 and 20 kbar and for durations 61 day. Theonly deformation of the material occurred during the filling ofthe experimental capsule prior to high pressure experiments (fold-ing of the wood tissue). Telinite and cell infilling brightened withrun duration during isobaric experiments at 10 and 20 kbar. Theoptical distinction between telinite and cell infilling became moredifficult with increasing run time. Hence, more attention wasneeded to distinguish telinite from the infilling of the cell lumensfor experiments with duration >1 day at 10 (Fig. 3g) and 20 kbar(Fig. 3d). However, the original cellular microstructure of the cy-press was still recognizable after 25 days of high pressure experi-mental maturation.

3.2. Vitrinite reflectance

VR results from dry (no water added) experiments at 400 �C andat three different pressures (2, 10 and 20 kbar) are presented inTable 1 and plotted in VR versus effective heating time t0 diagrams(Fig. 4). Besides our experimental results, we use published VR dataobtained at 2 kbar and 400 �C from a previous experimental studyby Ernst and Ferreiro Mählmann (2004) who experimented on thesame kind of starting material. They used humite from an angio-sperm lignite as starting material.

VR results from duplicated runs carried out in this experimentalprogram at various P–t0 conditions (Table 1 and Fig. 4) are consis-tent in most cases within the limits of experimental and measure-ment uncertainties and validates our techniques.

Table 1Experimental maturation conditions and results.a

Run no. Methodb P (bar) t0 (s) V

GE-V4 CSPV 2000 0 0GE-V3 CSPV 2000 900 0GE-V8 CSPV 2000 3600 1GE-V12 CSPV 2000 86,400 1GE-H28 CSPV 2000 1,555,200 2GE-F30 CSPV 2000 2,505,600 2GE-H30 CSPV 2000 2,505,600 2GE-F27 CSPV 2000 4,320,000 2GE-H27 CSPV 2000 4,320,000 2RLB-e43 HPPC 10,000 0 0RLB-e30 HPPC 10,000 100 0RLB-e39 HPPC 10,000 240 0RLB-e22 HPPC 10,000 900 0RLB-e33 HPPC 10,000 900 0RLB-e16 HPPC 10,000 3600 1RLB-e42 HPPC 10,000 3600 0RLB-e41 HPPC 10,000 8100 1RLB-e40 HPPC 10,000 18,000 1RLB-e27 HPPC 10,000 86,400 1RLB-e05 HPPC 10,000 432,000 2RLB-e19 HPPC 10,000 432,000 2RLB-e44 HPPC 10,000 2,160,000 2RLB-e84 HPPC 20,000 0 0RLB-e35 HPPC 20,000 900 0RLB-e26 HPPC 20,000 900 0RLB-e02 HPPC 20,000 3600 0RLB-e06 HPPC 20,000 3600 0RLB-e03 HPPC 20,000 18,000 1RLB-e08 HPPC 20,000 18,000 1RLB-e07 HPPC 20,000 86,400 1RLB-e04 HPPC 20,000 432,000 2RLB-e36 HPPC 20,000 432,000 2RLB-e01 HPPC 20,000 2,160,000 3

a Notations: P, pressure; t0 , experimental effective heating time; VR(P, 400 �C, t0), measupressure P; rVR(P, 400 �C, t0), standard deviation of VR(P, 400�C, t0); N, number of measurem

b HPPC, high pressure piston-cylinder apparatus experiments; CSPV, cold-seal pressurc Results of this study.d Results of Ernst and Ferreiro Mählmann (2004).

3.2.1. Effect of dry experimental maturation on VRPrior to detailed analysis of the changes in VR, we provide a gen-

eral observation concerning the maturation of Type III organic mat-ter in a dry (no water added) system. The first impression fromresults presented in Table 1 and Fig. 4a–c is that VR increases withrun time and with pressure at 400 �C. This observation is of primeimportance because it demonstrates that Type III organic mattermaturation occurs in the dry system and addition of water is notrequired at 400 �C. A similar observation has been reported byMonthioux et al. (1985), Landais et al. (1994) and Huang (1996).

3.2.2. Effect of experimental heat-up to T = 400 �C on VRTo date, no attention has been paid to the effect of experimental

heat-up procedures on organic matter maturation to the final runtemperature and pressure. This is surprising in the light of the sen-sitivity of organic matter maturation to temperature. For such anevaluation, we performed experiments at 2, 10 and 20 kbar, raisedthe temperature to 400 �C and quenched immediately. We mea-sured a significant increase in VR in all three run products (Table 1and Fig. 4a–c). From the immature starting material withVR = 0.17%, VR changes during the 8 min of heat-up time to0.504% at 20 kbar (RLB-e84) and 0.67% at 10 kbar (RLB-e43). At2 kbar and after 30 min of heat-up time VR = 0.745% (GE-V4). It isto be noted that, the vitrinite run products surpass the onset ofoil generation commonly fixed at VR = 0.5% (e.g., Taylor et al.,1998) after these very short heat-up times. These results demon-strate the strong effect of the experimental heat-up on vitrinitereflectance and therefore on organic matter maturation, even with

R(P, 400 �C, t0) (%) rVR(P, 400 �C, t0) N Source

.745 0.044 137 c

.753 0.039 442 c

.176 0.042 100 c

.624 0.048 101 c

.041 0.057 100 d

.086 0.094 34 d

.068 0.058 100 d

.116 0.072 41 d

.191 0.075 100 d

.669 0.034 239 c

.666 0.037 173 c

.683 0.047 116 c

.864 0.053 278 c

.862 0.038 100 c

.066 0.041 500 c

.952 0.054 500 c

.262 0.078 223 c

.386 0.031 263 c

.695 0.060 100 c

.098 0.037 167 c

.017 0.031 161 c

.561 0.057 235 c

.504 0.027 500 c

.681 0.033 136 c

.706 0.023 115 c

.860 0.024 100 c

.883 0.036 100 c

.129 0.039 137 c

.130 0.048 500 c

.879 0.034 100 c

.326 0.018 200 c

.130 0.053 100 c

.360 0.051 105 c

red vitrinite reflectance after an experimental effective heating time t0 at 400 �C andents.

e vessel experiments.

Page 7: LeBayon 2011 Organic-Geochemistry

t' (s)

VR( P

,400

°C, t

') (

%)

2000 3000 400010000

1.3

1.2

1.0

1.1

0.9

0.8

0.7

0.6

: VRheat-up (10 kbar,400 °C)

: VRheat-up (2 kbar,400 °C)

: 10 kbar: 2 kbar

d

: VRheat-up (20 kbar,400 °C)

VR( 2

0kba

r,40

0°C

,t')

(%

)

t' (days)

20 kbar

4.0

3.5

3.0

2.5

2.0

1.5

1.0

0.5

0.020 25 30105 150

c

t' (days)

VR(1

0kba

r,40

0°C

,t')

(%

)

20 25 30105 150

3.0

2.5

2.0

1.5

1.0

0.5

0.0: VRheat-up (10 kbar,400 °C)

10 kbar

b

t' (days)

VR( 2

kbar

,400

°C,t

') (

%)

40 50 602010 300

2.5

2.0

1.5

1.0

0.5

0.0

2 kbar

: VRheat-up (2kbar,400 °C)

a

r2 = 0.997 r2 = 0.996

r2 = 0.995

Fig. 4. Vitrinite reflectance VR as a function of experimental effective heating time t0 at 400 �C and (a) 2 kbar, (b) 10 kbar and (c) 20 kbar. The curves are the least-squares bestfits to the data using the power law equation VR(P, 400 �C, t0) = VR(P, 400 �C, 0) + (k0(P, 400 �C) t0)n0(P, 400 �C) (Eq. (1)). The heat-up vitrinite reflectance VRheat-up(P, 400 �C) (star) isshown at each investigated pressure for information but is excluded from this kinetic fit. VR data similar to their respective starting vitrinite reflectance VRheat-up(P, 400 �C) areneither plotted nor considered into this kinetic fit (see text). The error bars are ±one standard deviation rVR(P, 400 �C, t0). (d) VR(P, 400 �C, t0) of the shorter experimental effectiveheating times t0 as a function of t0 at 400 �C and 2 and 10 kbar. VR(P, 400 �C, t0) plateaus that indicate short activation time before VR increases from the starting vitrinitereflectance VRheat-up(P, 400 �C) are clearly visible.

346 R. Le Bayon et al. / Organic Geochemistry 42 (2011) 340–355

very short duration. This increase in VR during heat-up to 400 �C isdescribed as VRheat-up(P, 400 �C) below. This heat-up vitrinite reflec-tance VRheat-up(P, 400 �C) must be taken as the starting point in ourkinetic study and not the initial VR = 0.17% of the starting material.It is also important to note that VRheat-up(P, 400 �C) decreases withincreasing pressure.

3.2.3. Qualitative effects of effective heating time on VRThe results presented in Table 1 and Fig. 4a–c (diagrams of VR

versus t0) show an isobaric increase in VR with effective heatingtime at 400 �C and at each investigated pressure. The isobaric rateof VR increase is initially very rapid as seen from the steep positiveslopes of the VR versus t0 relation in Fig. 4a–c. Nevertheless, the re-duced slopes of the VR–t0 versus with t0 trend (Fig. 4a–c) indicateslowing of the rate of increase in VR with run duration at each pres-sure and thus a deceleration of VR enhancement with t0. Theseobservations confirm previous experimental results (Huang,1996; Ernst and Ferreiro Mählmann, 2004).

3.2.4. Qualitative effects of pressure on VRAs seen in Fig. 4a–c, pressure has a strong effect on the kinetics

of VR evolution. The isobaric–isothermal VR evolution trends witht0 show that the increase in VR with t0 is greatly enhanced withpressure. This observation is supported by the lesser reduction inVR–t0 slope with increasing pressure. It illustrates that increasingpressure leads to a lesser deceleration of VR enhancement with

time. These important qualitative observations on the effects ofpressure on VR evolution rates are further confirmed by the de-crease in VRheat-up(P, 400 �C) with pressure (see above). Conse-quently, elevated pressure counteracts the decrease in the rate ofVR increase with time. Evidently, pressure promotes VR increasefor Type III organic material, confirming our preliminary results(Le Bayon et al., 2007). The rate of vitrinite reflectance increase isnot only a thermally activated process, it is also pressurecontrolled.

3.2.5. Short activation timeThe results of experiments RLB-e30 and RLB-e39 at 10 kbar and

GE-V3 at 2 kbar (Table 1 and Fig. 4d) provide evidence for a shortactivation time before measurable maturation starts at 400 �C witha VRheat-up(P, 400 �C) starting material. No experimental activationtime was detected at 20 kbar. The existence of such an activationtime is demonstrated at 2 and 10 kbar by the plateaus of vitrinitereflectance data similar to their respective starting vitrinite reflec-tance VRheat-up(P, 400 �C) with increasing run duration at 400 �C.These plateaus indicate that at least 15 min at 2 kbar and 4 minat 10 kbar are required before a change in VR of the run materialis detected. However, it is impossible to deduce any trend in theactivation time evolution with pressure because the maturationexperiments are conducted with a starting material having differ-ent VRheat-up(P, 400 �C) at each experimental pressure. In addition,it is experimentally difficult to retrieve information on any

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R. Le Bayon et al. / Organic Geochemistry 42 (2011) 340–355 347

variation of the activation time with VRheat-up(P, 400 �C) evolutionof the starting material. Thus, the concept of activation time iscomplex. It is judicious to ignore any systematic treatment of theactivation time as a function of pressure or VRheat-up(P, 400 �C) inour kinetic analysis. Nevertheless, the VRheat-up(P, 400 �C) and acti-vation time effects on VR evolution with heating time and pressurehave to be corrected in our following kinetic analysis. Furthermore,the VRheat-up(P, 400 �C) data and the VR data showing the short acti-vation time before to detect an increase in maturation with runduration at each investigated pressure and 400 �C are excludedfrom the following kinetic analysis. This stems from the lack of pre-cise time constraints for the start of increase in maturation of aVRheat-up(P, 400 �C) starting material with run duration at eachpressure and 400 �C.

4. Kinetic analysis

4.1. Empirical rate equation for VR evolution

In order to quantify and understand the relationship betweenvitrinite reflectance, pressure and time, we performed a kineticanalysis of the experimental results. This analysis will be a usefultool for extrapolating vitrinite reflectance to geological situationsvia an empirical rate equation.

4.1.1. The basic rate equationWe obtained experimental VR data over a sufficiently wide

range of time to statistically discriminate a rate law that describesVR evolution with effective heating time. The experimental VR dataemployed for the kinetic analysis are given in Table 1. Neverthe-less, the starting vitrinite reflectance data VRheat-up(P, 400 �C) andthe VR data showing the short activation time before to detect anincrease in maturation with run duration at each investigated pres-sure and 400 �C were excluded from the following kinetic analysis(see above). Consequently, the VR data RLB-e84 at 20 kbar, RLB-e43, RLB-e30 and RLB-e39 at 10 kbar and GE-V4 and GE-V3 at2 kbar are not considered in the kinetic analysis. We best fit ourexperimental VR data over effective heating time at each run pres-sure P and 400 �C by least squares to an empirical equation of theform

VRðP;400 �C;t0Þ ¼ VRðP;400 �C;0Þ þ ðk0ðP;400 �CÞt0Þn0ðP;400 �CÞ ð1Þ

where VR(P, 400 �C, t0) is the vitrinite reflectance value after effec-tive heating time t0 (s), VR(P, 400 �C, 0) is the original vitrinite reflec-tance at t0 = 0, k0(P, 400 �C) is the rate constant with dimensions[time]�1 and n0(P, 400 �C) is the dimensionless exponent at a givenpressure P and 400 �C. The exponent n0(P, 400 �C) has no signifi-cance in terms of stoichiometries of the chemical reaction mecha-nisms. The experimental VR data were weighted assuming theuncertainties in measured VR given in Table 1. Eq. (1) provides a sat-isfactory description of our VR data as all fits yield correlation coef-ficients r2 > 0.995 (Table 2). In Table 2, we provide the magnitudesof VR(P, 400 �C, 0), k0(P, 400 �C) and n0(P, 400 �C) that were deter-mined at each run pressure P by fitting the experimental VR data(Table 1) to Eq. (1). We plotted the three isobaric least squaresregression curves in VR(P, 400 �C, t0) versus t0 diagrams (Fig. 4a–c).

Table 2Vitrinite reflectances at effective heating time t0 = 0 VR(P, 400 �C, t0 = 0), rate constants k0(P

P (bar) VR(P, 400 �C, t0 = 0) (%) rVR(P, 400 �C, t0=0) k0(P, 400 �C) (s�1

2000 �1.426 � 10+2 2.030 6.675 � 10+160

10,000 �6.390 � 10�1 6.078 � 10�1 6.678 � 10�23

20,000 2.788 � 10�1 6.250 � 10�2 6.558 � 10�13

a Notations: rVR(P, 400 �C, t0=0), standard deviation of VR(P, 400 �C, t0 = 0); rk0(P, 400 �C), stacorrelation coefficient.

These curves show the expected larger increase in VR with timeand the lesser deceleration with time of VR isothermal increase withincreasing pressure that were described above. In addition, thesecurves display the very short activation times that were notedabove (Fig. 4d).

Despite the excellent correlation coefficients obtained by usingEq. (1) to fit the experimental results, caution is required to extrap-olate this rate equation to nature or to compare the kinetic param-eters in Table 2. Indeed, we have pointed out above that thevitrinite maturation rate experiments at 400 �C and fixed pressurewere conducted using a starting material having vitrinite reflec-tance VRheat-up(P, 400 �C). This value was gained during the exper-imental heat-up to 400 �C at pressure P. Therefore, Eq. (1)describes the evolution of VR with time and pressure at 400 �Cfor a starting material with vitrinite reflectance VRheat-up(P,400 �C). In addition, the 2 and 10 kbar runs have an activationtime before detecting maturation. This activation time effect isdefined for a VRheat-up(P, 400 �C) and a pressure P. Therefore, theVRheat-up(P, 400 �C) and activation time effects restrict the applica-bility of Eq. (1) for geological settings. Consequently, we must cor-rect Eq. (1) for the VRheat-up(P, 400 �C) and activation time effects.

4.1.2. Corrections to the basic rate equationTo overcome the VRheat-up(P, 400 �C) and activation time effects,

our strategy is based on an analytical correction of Eq. (1) resultingfrom two considerations. First, it is experimentally impossible toget vitrinite reflectance below VRheat-up(P, 400 �C) because this VRwas obtained for the experimental effective heating time t0 = 0 s.Second, we have no information about the activation time evolu-tion with pressure and with the same starting material afterheat-up to 400 �C.

We define a new base of effective heating time, t, which permitsquantification of VR evolution versus corrected effective heatingtime t with a starting VR equal to 0% at t = 0, i.e. VR(P, 400 �C,t = 0) = 0%. This is done by adding or subtracting time to the t0 baseat each pressure so that a power law equation similar to Eq. (1) hasits original VR at t = 0 (VR(P, 400 �C, t = 0)) equal to 0%. We arbi-trarily define the starting VR equal to 0% at t = 0 despite the factthat the vitrinite precursor has a reflectance ranging between�0.1 and �0.2%. The choice to fit our experimental data and to for-mulate a VR evolution rate equation with a starting VR equal to 0%allows a practical VR calculation from any value of starting VR withour VR evolution rate equation once a simple correction of theheating time is performed (see Section 4.4).

Finally, corrections for the VRheat-up(P, 400 �C) and activationtime effects require the addition of �15 s to t0 at 20 kbar and sub-traction of �430 s from t0 at 10 kbar and �2780 s from t0 at 2 kbarin order to transform the effective heating time t0 base to the cor-rected effective heating time t base. We list in Table 3 the correctedeffective heating time t for the VR data considered in the kineticanalysis, i.e., VR data showing an increase in maturation fromVRheat-up(P, 400 �C) (see above).

4.1.3. The rate equation for VR evolutionHaving corrected the effective heating time for the activation

time problem and for the VRheat-up(P, 400 �C) effect, we are now

, 400 �C) and power law exponents n0(P, 400 �C) at pressures P and 400 �C.a

) rk0(P, 400 �C) (s�1) n0(P, 400 �C) rn0(P, 400 �C) r2

1.790 � 10+308 9.586 � 10�4 3.848 � 10�5 0.9975.648 � 10�22 9.477 � 10�2 2.694 � 10�2 0.9965.014 � 10�13 2.584 � 10�1 1.521 � 10�2 0.995

ndard deviation of k0(P, 400 �C); rn0(P, 400 �C), standard deviation of n0(P, 400 �C); r2,

Page 9: LeBayon 2011 Organic-Geochemistry

Table 3Experimental maturation conditions and results after corrections of the effective heating time.a

Run no. P (bar) t (s) VR(P, 400 �C, t) (%) rVR(P, 400 �C, t) ln t (t in s) ln VR(P, 400 �C, t)

GE-V8 2000 820 1.176 0.042 6.709 �4.443GE-V12 2000 83,620 1.624 0.048 11.334 �4.120GE-H28 2000 1,552,420 2.041 0.057 14.255 �3.892GE-F30 2000 2,502,820 2.086 0.094 14.733 �3.870GE-H30 2000 2,502,820 2.068 0.058 14.733 �3.879GE-F27 2000 4,317,220 2.116 0.072 15.278 �3.856GE-H27 2000 4,317,220 2.191 0.075 15.278 �3.821RLB-e22 10,000 470 0.864 0.053 6.153 �4.751RLB-e33 10,000 470 0.862 0.038 6.153 �4.754RLB-e16 10,000 3170 1.066 0.041 8.061 �4.541RLB-e42 10,000 3170 0.952 0.054 8.061 �4.654RLB-e41 10,000 7670 1.262 0.078 8.945 �4.372RLB-e40 10,000 17,570 1.386 0.031 9.774 �4.279RLB-e27 10,000 85,970 1.695 0.060 11.362 �4.077RLB-e05 10,000 431,570 2.098 0.037 12.975 �3.864RLB-e19 10,000 431,570 2.017 0.031 12.975 �3.904RLB-e44 10,000 2,159,570 2.561 0.057 14.585 �3.665RLB-e35 20,000 915 0.681 0.033 6.819 �4.989RLB-e26 20,000 915 0.706 0.023 6.819 �4.953RLB-e02 20,000 3615 0.860 0.024 8.193 �4.756RLB-e06 20,000 3615 0.883 0.036 8.193 �4.730RLB-e03 20,000 18,015 1.129 0.039 9.799 �4.484RLB-e08 20,000 18,015 1.130 0.048 9.799 �4.483RLB-e07 20,000 86,415 1.879 0.034 11.367 �3.974RLB-e04 20,000 432,015 2.326 0.018 12.976 �3.761RLB-e36 20,000 432,015 2.130 0.053 12.976 �3.849RLB-e01 20,000 2,160,015 3.360 0.051 14.586 �3.393

a Notations: P, pressure; t, corrected effective heating time; VR(P, 400 �C, t), measured vitrinite reflectance at the corrected effective heating time t, 400 �C and pressure P;rVR(P, 400 �C, t), standard deviation of VR(P, 400 �C, t).

348 R. Le Bayon et al. / Organic Geochemistry 42 (2011) 340–355

in a position to accommodate an initial vitrinite reflectance valuein our fit. Hence, we plot in Fig. 5 and best fit our experimentalVR(P, 400 �C, t) data without the VRheat-up(P, 400 �C) data and theVR data similar to their respective starting vitrinite reflectanceVRheat-up(P, 400 �C) (see above) over corrected effective heatingtime (Table 3) at each run pressure P by least squares to a powerlaw equation of the form

VRðP;400 �C;tÞ ¼ ðkðP;400 �CÞtÞnðP;400 �CÞ ð2Þ

where VR(P, 400 �C, t) is the vitrinite reflectance value attained aftercorrected effective heating time t (s), k(P, 400 �C) is the rate con-stant with dimensions [time]�1 and n(P, 400 �C) is the dimension-less exponent at a given pressure P and 400 �C. This rate equation

20 kbar10 kbar

2 kbar

r2 = 0.994

r2 = 0.997

r2 = 0.997

4.0

3.5

3.0

2.5

2.0

1.5

1.0

0.5

0.0

VR(P

,400

°C,t

) (%

)

20 30 40 50100

t (days)

20 kbar

2 kbar

10 kbar

400 °C

Fig. 5. Variation in vitrinite reflectance VR(P, 400 �C, t) with corrected effectiveheating time t at 400 �C and 2, 10 and 20 kbar (Table 3). The curves are theleast-squares best fits to the data using the power law equation VR(P, 400 �C, t) =(k(P, 400 �C) t) n(P, 400 �C) (Eq. (2)). The error bars are ±one standard deviationrVR(P, 400 �C, t).

is defined for a starting VR equal to 0% at t = 0. The experimentalVR data were weighted assuming the uncertainties in measuredVR given in Table 3. Table 4 lists the magnitudes of k(P, 400 �C)and n(P, 400 �C) that were determined at each run pressure P by fit-ting the (VR(P, 400 �C, t), t) data in Table 3 to Eq. (2). We plot thethree isobaric least squares regression curves in the VR(P, 400 �C,t) versus t diagram (Fig. 5). Eq. (2) provides a satisfactory descrip-tion of our VR data with time inasmuch as the fits all yield correla-tion coefficients r2 > 0.994 (Table 4). However, to validate ourpower law Eq. (2) to fit the experimental data, we transformedthe nonlinear relation between VR(P, 400 �C, t) and t into a linearrelation. To effect the desired linearization, we simply take the nat-ural logarithm of Eq. (2), yielding

ln VRðP;400 �C;tÞ ¼ nðP;400 �CÞ ln kðP;400 �CÞ þ nðP;400 �CÞ ln t

ð3Þ

where n(P, 400 �C) is the slope and n(P, 400 �C) ln k(P, 400 �C) is thenormalization constant of the straight line ln VR(P, 400 �C, t) versusln t. The straight lines are calculated using Eq. (3) at 2, 10 and20 kbar, using the best estimates for the constants n(P, 400 �C)and k(P, 400 �C) given in Table 4. Results of these calculations arepresented in Fig. 6. Fig. 6 is a ln VR(P, 400 �C, t) versus ln t plot thatgives a set of three lines of ln VR(P, 400 �C, t) evolution with ln t atthree different pressures. The pairs (ln VR(P, 400 �C, t), ln t) (Table 3)are found to lie on or close to the straight lines shown in Fig. 6. Thisgraphic check demonstrates that the variables ln VR(P, 400 �C, t) andln t are linearly related. This result confirms the use of our powerlaw equation (Eq. (2)) to describe the evolution of vitrinite reflec-tance with time at different pressures and 400 �C. In addition, thislinear Eq. (3) and its plot in Fig. 6 are useful because they show thatboth short (65 days) and long (>5 days) duration experiments areimportant to quantify VR evolution with heating time. Furthermore,this kinetic analysis shows that VR evolution is continuous withheating time.

We are now in a position to discuss the VR magnitude andkinetics because Eqs. (2) and (3) and their related VR–t data

Page 10: LeBayon 2011 Organic-Geochemistry

Table 4Rate constants k(P, 400 �C) and power law exponents n(P, 400 �C) at pressures P and 400 �C.a

P (bar) k(P, 400 �C) (s�1) rk(P, 400 �C) (s�1) n(P, 400 �C) rn(P, 400 �C) r2

2000 9.541 � 10�31 3.337 � 10�30 7.120 � 10�2 4.460 � 10�3 0.99710,000 1.648 � 10�19 1.523 � 10�19 1.282 � 10�1 3.780 � 10�3 0.99720,000 2.782 � 10�14 7.894 � 10�15 2.062 � 10�1 3.101 � 10�3 0.994

a Notations: rk(P, 400 �C), standard deviation of k(P, 400 �C); rn(P, 400 �C), standard deviation of n(P, 400 �C); r2, correlation coefficient.

lnVR

(P,4

00°C

, t)

ln t (t in s)

3.5

4.0

4.5

5.0

6 8 10 12 14 16

15min

3min 1 h 5 h 1 d

t

5 d 25 d4.0

3.0

2.5

2.0

1.5

1.2

1.0

0.6

0.8

VR(P,400

°C,t )

(%)

20 kbar10 kbar

2 kbar

r220 kbar = 0.994

r210 kbar = 0.997

r22 kbar = 0.997

2 kbar

20 k

bar

10 kb

ar

400 °C

100 d

Fig. 6. Double-logarithmic plot of the vitrinite reflectance VR(P, 400 �C, t) versuscorrected effective heating time t at 400 �C and 2, 10 and 20 kbar (Table 3). Thestraight lines are calculated at 2, 10 and 20 kbar, using the linear equation ln VR(P,400 �C, t) = n(P, 400 �C) ln k(P, 400 �C) + n(P, 400 �C) ln t (Eq. (3)) and the bestestimates for the constants n(P, 400 �C) and k(P, 400 �C) given in Table 4.

4 3 5 6

20

25

15

10

5

lnVR (VR in %)

VR (%)

ln

dVR( P,400°C

,t )/dt(%

.s1)

(dVR

(P,4

00°C

,t)

/dt)

10 3

10 1

10 7

10 5

2.50.4 4.01.441.00.6

10 kbar

20 kbar

2 kbar

400 °C

Fig. 7. Double-logarithmic plot of the variation in the rate at which VR(P, 400 �C, t)increases with time versus VR at 400 �C and 2, 10 and 20 kbar. The lines arecalculated using the equation ln (dVR(P, 400 �C, t)/dt) = ln (n(P, 400 �C) k(P,400 �C))+ (1 � n(P, 400 �C)�1) ln VR(P, 400 �C, t) (Eq. (5)) and the best estimates for theconstants n(P, 400 �C) and k(P, 400 �C) given in Table 4. ln VR(P, 400 �C, t) is given byEq. (3). The three lines intersect at VR = 1.44% and dVR(P, 400 �C, t)/dt = 7.00 � 10�6 % s�1.

R. Le Bayon et al. / Organic Geochemistry 42 (2011) 340–355 349

(Table 3) are defined for a starting VR equal to 0% at t = 0. Fig. 6points out that the highest initial VR magnitude and evolutionkinetics occur at the lowest pressure. This reveals that pressure re-tards the initial VR increase at 400 �C. Furthermore, the increase inVR decelerates with increasing time. However, Figs. 5 and 6 con-firm our qualitative observations reported above for t > �15 h. Inparticular, pressure enhances VR increase with time. This calls fora lesser deceleration of VR increase with increasing pressure.

These observations show that the role of pressure on VR isimportant and complex. It is essential to accurately analyze the ef-fects of pressure on VR increase kinetics. For this purpose, we as-sess the effects of pressure on the rate at which VR increaseswith time for each VR magnitude. The rate at which VR increaseswith time at each pressure is found by differentiating Eq. (2) withrespect to time, yielding

dVRðP;400 �C;tÞ=dt ¼ nðP;400 �CÞkðP;400 �CÞnðP;400 �CÞtnðP;400 �CÞ�1

ð4Þ

Taking the natural logarithm of Eq. (4) for graphic convenienceand using k(P, 400 �C)�1 VR(P, 400 �C, t)�n(P, 400 �C) in place of t froma rearrangement of Eq. (2), we obtain by rearranging andsimplifying

lnðdVRðP;400 �C;tÞ=dtÞ ¼ lnðnðP;400 �CÞkðP;400 �CÞÞ þ ð1

� nðP;400 �CÞ�1Þ ln VRðP;400 �C;tÞ ð5Þ

We calculate the linear Eq. (5) at 2, 10 and 20 kbar using thebest estimates for the constants n(P, 400 �C) and k(P, 400 �C) givenin Table 4. The evolution of ln (dVR(P, 400 �C, t)/dt) versus ln VR ateach pressure is presented in Fig. 7. Obviously, the rate of VR in-crease decreases with VR at each pressure (Fig. 7). This argues forthe deceleration with heating time of VR increase at each pressurethat is described above and shown in Figs. 5 and 6. Nevertheless,Fig. 7 shows that increasing pressure results in the lesser deceler-ation of VR enhancement with VR and thus with heating time. Thisleads the evolutions of the rate of VR increase with VR at 2, 10 and20 kbar to intersect at VR = 1.44%. This calls for a variation in theeffects of pressure on the VR increase kinetics. When VR < 1.44%,Fig. 7 demonstrates that increasing pressure diminishes the rateof VR increase. Hence, increasing pressure results in the retardationof the initial VR enhancement with heating time that is displayedfor t < �15 h in Fig. 6. Consequently, the lower pressure, the higherare the initial VR magnitude and evolution kinetics. Nevertheless,the retarding effect of pressure on VR enhancement decreases withincreasing VR and thus with heating time. This is inferred from thedecrease of the difference between the rates of VR increase at dif-ferent pressure (Fig. 7). When VR > 1.44%, Fig. 7 indicates that pres-sure reduces the decrease in the rate of VR increase occurring withenhancing VR. This points out that pressure counteracts the decel-eration of VR increase with time. Therefore, increasing pressureleads to the larger enhancement of VR increase with time whenVR > 1.44%. This is supported by the VR–t evolutions presented inFigs. 5 and 6 when t > �15 h. To sum up, pressure retards the

Page 11: LeBayon 2011 Organic-Geochemistry

n(P,

400°

C)

P (kbar)

0.05

0.00

0.10

0.15

0.20

0.25

0.30

2510 201550

r2 = 0.999

400 °C

Fig. 8. Variation in power law exponent n(P, 400 �C) with pressure at 400 �C(Table 4). The solid line is the least-squares best fit to the data using the linearequation n(P, 400 �C) = n(0, 400 �C) + BP (Eq. (6)). The error bars in n(P, 400 �C) are±one standard deviation rn(P, 400 �C). The error bars in pressure are ±25 bar at 2 kbarand ±1 kbar at 10 and 20 kbar.

350 R. Le Bayon et al. / Organic Geochemistry 42 (2011) 340–355

maturation of vitrinite when VR < 1.44% and promotes it whenVR > 1.44%. However, a VR of 1.44% is attained after a very shortheating time t of �12 h at 20 kbar, �7 h at 10 kbar and �4 h at2 kbar and 400 �C from a starting VR equal to 0%. Thus, the retarda-tion of VR increase is insignificant for vitrinite maturation occur-ring in geological setting at 400 �C. Consequently, pressurepromotes VR for geological heating time at 400 �C, even thoughpressure retards the initial VR evolution kinetics.

Several key features of the evolution of the constants n(P,400 �C) and k(P, 400 �C) with pressure are evident from Fig. 6. Inparticular, the three non-parallel lines of the ln VR(P, 400 �C, t) evo-lution with ln t exhibit different positive slopes n(P, 400 �C) thatare observed to increase with pressure having magnitudes rangingbetween 0.07 and 0.21 (Table 4). The normalization constants n(P,400 �C) ln k(P, 400 �C) decrease with increasing pressure. Never-theless, the rate constants k(P, 400 �C) increase with pressure (Ta-ble 4). The power law (Eq. (2)) and the linear (Eq. (3)) equationswith their associated constants n(P, 400 �C) and k(P, 400 �C) sup-port all of the qualitative observations reported above and can beobserved in Fig. 6. In particular, these two equations accurately de-scribe the expected increase in VR with time at each investigatedpressure because n(P, 400 �C) > 0. Nevertheless, they call for a de-crease in the rate of VR isobaric increase with time as n(P,400 �C) < 1. However, Eqs. (2) and (3) support that enhancing pres-sure results in a lesser deceleration of VR increase with time be-cause n(P, 400 �C) increases with pressure. Furthermore, thehigher pressure, the lower are the initial VR magnitude and evolu-tion kinetics because the normalization constant n(P, 400 �C) lnk(P, 400 �C) decreases with increasing pressure.

To describe the VR evolution rates at different temperatures andpressures, Huang (1996), Dalla Torre et al. (1997) and Ernst andFerreiro Mählmann (2004) favored an empirical rate equation inthe form of VR = ktn where t is time, k is a rate constant and n a con-stant unchanged over the experimental temperature and pressurerange. Even though this rate equation satisfactorily describes theirexperimental data, we consider these studies to be limited becausethey do not consider the activation time and experimental heat-upeffects and their associated corrections to the VR evolution rateequation.

Results reported here emphasize the important role of n(P,400 �C) and k(P, 400 �C) in the power law Eq. (2) and in its lineartransformation (Eq. (3)) to control the kinetic evolution of VR in-crease with time and pressure. Hence, we must next assess thepressure dependence of n(P, 400 �C) and k(P, 400 �C).

4.2. Pressure dependence of the power law exponent n(P, 400 �C)

Initially, the power law exponent was considered to be indepen-dent of pressure (Dalla Torre et al., 1997) and temperature (Huang,1996; Dalla Torre et al., 1997; Ernst and Ferreiro Mählmann, 2004).In contrast, we have previously noted that the power law exponentn(P, 400 �C) increases with pressure. Therefore, it is of particularinterest to analyze the influence of pressure on this variable.Accordingly, we plot n(P, 400 �C) (Table 4) versus pressure inFig. 8: A regular increase in the power law exponent with pressureis evident. This graphically points out the linear pressure depen-dence of this exponent. We best fit all the data in Fig. 8 to quantifythe variation of the power law exponent n(P, 400 �C) as a function ofpressure P by least squares to a linear relation expressed as

nðP;400 �CÞ ¼ nð0;400 �CÞ þ BP ð6Þ

where the constant B with dimensions [bar]�1 is the slope of theregression line of n(P, 400 �C) on P and the constant n(0, 400 �C) isthe dimensionless power law exponent at which the pressurewould drop to zero at 400 �C. The data are weighted assuming theuncertainties in n(P, 400 �C) given in Table 4. The power law

exponent n(P, 400 �C) is successfully linearly related to P with acorrelation coefficient r2 > 0.999. We best estimate at 400 �C thetwo constants in Eq. (6) as n(0, 400 �C) = 5.46 (±0.43) � 10�2 andB = 7.55 (±0.30) � 10�6 bar�1. The line of regression of the powerlaw exponent n(P, 400 �C) on pressure P is plotted in Fig. 8.

The demonstration that n(P, 400 �C) increases linearly withpressure is of major importance to quantify the evolution of vitri-nite reflectance with time and pressure. It confirms all the pressureeffects observed above on the rate of VR increase with time bymeans of n(P, 400 �C). Furthermore, the recognition that n(P,400 �C) is a function of pressure begins to make apparent the pres-sure contribution to the rate Eq. (2).

4.3. Pressure dependence of the rate constant k(P, 400 �C)

In addition to n(P, 400 �C), the rate constant k(P, 400 �C) seemsalso to account for the pressure effect because k(P, 400 �C) also var-ies with P. The k(P, 400 �C) data are presented in Table 4 and areplotted versus pressure P in Fig. 9a. The key feature revealed by Ta-ble 4 and by Fig. 9a is the huge increase in the rate constant k(P,400 �C) with pressure. We quantify the k(P, 400 �C) variation as afunction of pressure P by best fitting the k(P, 400 �C) data over Pby an empirical power law equation in the form of

kðP;400 �CÞ ¼ CPD ð7Þ

where C is a constant at 400 �C with dimensions [bar]�D [time]�1 andD is the dimensionless exponent that characterizes the evolution ofk(P, 400 �C) with P at 400 �C. The data were weighted assuming theuncertainties in k(P, 400 �C) given in Table 4. The best estimates forthe two constants of Eq. (7) are C = 8.514 (±108.89) � 10�89 bar�D s�1

and D = 17.325 (±1.245). Hence, the exponent D supports the ob-served increase in the rate constant k(P, 400 �C) with pressure(Fig. 9a) inasmuch as D > 0. The relationship between the variablesk(P, 400 �C) and P is successfully described by the power law Eq. (7)because this fit shows a correlation coefficient r2 of 0.995. Despite thisexcellent correlation coefficient, it is useful to test the fit for the k(P,400 �C) data over pressure with a power law equation. For this pur-pose, we convert the nonlinear relation Eq. (7) to a linear one by tak-ing its natural logarithm to give

ln kðP;400 �CÞ ¼ ln C þ D ln P ð8Þ

where D is the slope and ln C is the normalization constant of thestraight line ln k(P, 400 �C) versus ln P. The straight line is calculated

Page 12: LeBayon 2011 Organic-Geochemistry

70

80

60

50

40

30

20

9 1087

lnk

(P,4

00°C

)

lnP (P in bar)

P (kbar)

P (kbar)

202 10

b

r2 = 0.995

k(P,

400°

C)×

1014

(s1 )

0

1

2

3

4

2510 201550

r2 = 0.995

a

10 19

10 14

10 30

k(P, 400°C

) (s1)

400 °C

400 °C

Fig. 9. (a) Variation in the rate constant k(P, 400 �C) as a function of pressure at400 �C (Table 4). The solid curve is least-squares best fit to the data using the powerlaw equation k(P, 400 �C) = C PD (Eq. (7)). The error bars in k(P, 400 �C) are ±onestandard deviation rk(P, 400 �C). The error bars in pressure are ±25 bar at 2 kbar and±1 kbar at 10 and 20 kbar. (b) Double-logarithmic plot of the rate constant k(P,400 �C) versus P at 400 �C. The solid line is the calculated linear equation ln k(P,400 �C) = ln C + D ln P (Eq. (8)).

R. Le Bayon et al. / Organic Geochemistry 42 (2011) 340–355 351

with Eq. (8), using the best estimates for the constants C and D givenabove. A plot of this calculated straight line and of the negative re-trieved ln k(P, 400 �C) data versus ln P is shown in Fig. 9b. This plotdisplays a good fit of the data to the calculated straight line (Eq. (8))inasmuch as the pairs (ln k(P, 400 �C), ln P) lie on or close to thisstraight line. This graphic check validates the linear relationship be-tween ln k(P, 400 �C) and ln P. Therefore, the use of a power lawequation (Eq. (7)) is confirmed to describe the increase in the rateconstant k(P, 400 �C) with P at 400 �C. The pressure sensitivity dem-onstration of the rate constant k(P, 400 �C) is of interest because itfurther makes apparent the pressure contribution to the VR evolu-tion rate Eq. (2).

4.4. The pressure sensitive VR evolution rate equation – discussion

Having defined the pressure dependence of the power law expo-nent n(P, 400 �C) and the rate constant k(P, 400 �C), we are now in aposition to make explicit the pressure effect on the VR evolutionkinetics. In this regard, we insert Eqs. (6) and (7) in Eq. (2) to get

VRðP;400 �C;tÞ ¼ ðCPDtÞnð0;400 �CÞþBP ð9Þ

We now have an expression for the variation of VR with timeand pressure at 400 �C for Type III organic matter with initial

VR = 0%. Kinetic models that do not consider effects of pressure,effective heating time and heat-up to the final temperature maynot accurately account for the evolution of vitrinite reflectance innatural systems. Our experiments require further investigationsat different temperatures in order to formulate a general equationfor vitrinite reflectance evolution as a function of pressure, temper-ature and time. Hence, we regard our kinetic formulation as a steptoward this general equation. Such a P–T–t general equation wouldlead to different pathways to calculate VR in agreement with mea-sured values. Thus, VR cannot be converted directly into paleo-P–T–t conditions. Nevertheless, the number of possible solutions isgreatly diminished if information is available on temperature(e.g., microthermometry based on fluid inclusions, geothermalinvestigations) and/or pressure (barometry on adjacent calc-sili-cate rocks) attained and/or the heating time maintained duringmaturation (e.g., burial history in sedimentary basins, dating ofmetamorphic minerals). This opens the possibility to use VR as atool to estimate the P–T–t history of vitrinite bearing terranes byiteration based modeling. Calibration of the P–T–t history of vitri-nite bearing terranes will be a great help to gain insight into theirgeodynamic evolution and to improve hydrocarbon generationmodeling. Such tasks will be the subject of forthcomingcommunications.

4.4.1. How to use the power law formalism to model VRIt is of interest to make explicit how the power law formalism

has to be used to model VR for complex starting VR and P–T–t his-tories. This aims to avoid any misunderstanding and misuse ofsuch an equation. For this purpose, we postulate that the generalVR evolution rate equation obeys

VRðP; T; tÞ ¼ ðkðP; TÞtÞnðP;TÞ ð10Þ

where the rate constant k(P, T) and the power law exponent n(P, T)are both pressure and temperature dependent. This stems from thedemonstration that VR evolution is characterized by a power lawrate equation dependent on pressure (this study) and temperature(Huang, 1996; Dalla Torre et al., 1997 and Ernst and Ferreiro Mähl-mann, 2004). Furthermore, the kinetic parameters associated to thispower law formalism are pressure (this study) and temperaturedependent (Huang, 1996; Dalla Torre et al., 1997 and Ernst andFerreiro Mählmann, 2004). The power law equation quantifyingVR evolution (e.g., our isothermal VR evolution rate Eq. (9)) is re-trieved and formulated for a starting VR equal to 0% at t = 0. Conse-quently, the power law formalism with its associated rate constantk and power law exponent n must be used to calculate VR only for astarting VR equal to 0%. In nature, vitrinite precursors have reflec-tance ranging between �0.1 and �0.2%. In addition, the startingVR can display higher values resulting from one or several matura-tion events. However, the power law formalism (Eq. (10)) permitsthe evaluation of VR attained after any heating time theating at P–Tconditions (i.e., P2–T2) different from the previous ones (i.e.,P1–T1) (Fig. 10) from any starting VR once a correction for heatingtime is performed. For such VR estimation, we have to proceed intwo steps. First, we define the heating time tstarting necessary atP2–T2 to increase VR from 0% to any starting VR previously reachedat P1–T1 (i.e., VR(P1, T1)) (Fig. 10) with the power law Eq. (10) rear-ranged as

tstarting ¼ VRðP1; T1Þ�nðP2 ;T2Þ=kðP2; T2Þ ð11Þ

Second, VR attained after a heating time theating at P2–T2

(i.e., VR(P2, T2)) from any starting VR previously reached at P1–T1

(i.e., VR(P1, T1)) is defined by the power law formalism (Eq. (10))as VR attained after a corrected heating time equal totstarting + theating from a starting VR equal to 0% at P2–T2 (Fig. 10). Thisis formulated as

Page 13: LeBayon 2011 Organic-Geochemistry

t

VR

P2 T2

tstarting

theating

tstarting + theating

: any starting VR obtained at P1 T1

: VR attained after any heating time theating at P2 T2 from any starting VR

: starting VR equal to 0%

: VR t evolution at conditions P2 T2

0

00

1

1

2

1

2

Fig. 10. Sketch to illustrate how the power law formalism has to be used tocalculate VR for any starting VR and complex P–T–t history (see text).

t (days)

VR(1

0 kba

r,40

0°C

,t)

(%

)

20 25 30105 150

3.0

2.5

2.0

1.5

1.0

0.5

0.0

10 kbar

b

VR( 2

0kba

r,40

0°C

,t)

(%

)

t (days)

20 kbar

4.0

3.5

3.0

2.5

2.0

1.5

1.0

0.5

0.020 25 30105 150

c

t (days)6020 40 5010 300

VR( 2

kbar

, 400

°C,t

)

(%)

2.5

3.0

2.0

1.5

1.0

0.5

0.0

2 kbar

a

: EASY%Ro

: EASY%Ro

: EASY%Ro

Fig. 11. Comparison of VR modeled with EASY%Ro to VR obtained with experiments(Table 3) as a function of effective heating time t at 400 �C and (a) 2 kbar, (b) 10 kbarand (c) 20 kbar. The gray thick curves are VR evolution with time modeled withEASY%Ro at 400 �C. The light curves are the least-squares best fits to the data usingthe power law Eq. (2) that are displayed in Fig. 5. The error bars are ±one standarddeviation rVR(P, 400 �C, t).

352 R. Le Bayon et al. / Organic Geochemistry 42 (2011) 340–355

VRðP2; T2Þ ¼ kðP2; T2Þðtheating þ tstartingÞ� �nðP2 ;T2Þ ð12Þ

where tstarting is given by Eq. (11).This demonstrates the potential of application of the power law

formalism to model VR from any starting VR and for complex P–T–thistories. Furthermore, this brings out that the power law formal-ism is a simple and fast algorithm to calculate VR.

4.4.2. Our experimental VR data and empirical rate equation:Advantages, limitations and comparisons with other equations

Application of our empirical equation to Type I or II organicmatter is hazardous because these materials have different compo-sitions. Indeed, Types I and II organic matter have high hydrogencontents that inhibit VR enhancement.

Our VR rate equation is empirical and based on VR measuredafter experimental maturation of vitrinite at 400 �C under variouspressure and heating time conditions. Our rate equation is notbased on chemical kinetics because the chemical reactions in or-ganic matter/vitrinite maturation are complex. Nevertheless, ourobservations on VR evolution and our empirical VR kinetic equationare only valid at 400 �C. Further experimental investigations at dif-ferent temperatures are necessary in order to understand the ef-fects of pressure and time on VR at various temperatures and toformulate a general equation for VR evolution as a function of pres-sure, temperature and time. Such a general equation will be a use-ful tool to model the VR–T–t conditions in vitrinite bearingsedimentary basins and to estimate the P–T–t conditions in vitri-nite bearing metamorphic terranes occurring in various tectonicsettings. For this purpose, our power law formalism has the advan-tage to be a simple and fast algorithm to model VR–P–T–t evolutionin complex geological systems. This is of special interest in largescale basin simulations that have to be performed and repeatedmany times.

The earlier VR equations have several limitations. Barker (1983)and Barker and Pawlewicz (1986) developed a VR equation basedon a statistical relationship between measured VR and temperatureprofiles in sedimentary basins. They argued that the geologicaltemperature regime is sufficient to obtain a stable VR. Hence, theyignored the effect of heating time. However, we demonstrate inthis study that heating time is crucial in VR enhancement at

400 �C, even though we recognize a deceleration of the increasein VR with time. For example, we calculate a VR equal to 6.82% at400 �C using the equation of Barker and Pawlewicz (1986) (lnVR = 0.0078 Tmax(�C) – 1.2). To attain such a VR of 6.82 ± 0.2% withour VR rate Eq. (9), maturation at 400 �C requires a heating time t of6–13 Ma at 2 kbar, �475(±100) years at 10 kbar and �6(±1) yearsat 20 kbar. Maturation with heating times other than those calcu-lated using rate Eq. (9) displays different VR values from those cal-culated using the equation of Barker and Pawlewicz (1986). Thisshows the limitations of the Barker and Pawlewicz VR equation

Page 14: LeBayon 2011 Organic-Geochemistry

R. Le Bayon et al. / Organic Geochemistry 42 (2011) 340–355 353

at 400 �C despite the VR plateau calculated with our rate Eq. (9) forgeological heating times (6–13) at 2 kbar and 400 �C that approxi-mates the VR calculated with the equation of Barker and Pawlewicz(1986). Nevertheless, Ernst and Ferreiro Mählmann (2004) showthat the VR increase at 2 kbar and 200 �C is stabilized rapidly withheating time. Their long duration laboratory results demonstratethat at constant P–T conditions, a quasi-threshold VR value isattained in a geologically insignificant time and thereafter VRincreases progressively more slowly with continued heating. Thus,the equation of Barker and Pawlewicz (1986) might be relevant atvery low temperature conditions where the effects of time andpressure should be less pronounced on the VR evolution rates.

Larter (1989) provided a VR equation based on the concentra-tion of phenols released from vitrinite at different maturities dur-ing pyrolysis. A serious limitation of this approach is that theamounts of phenols released from organic matter are easily quan-tified only in the range 0.45% < VR < 1.6%. Another equation is theEASY%Ro method (Burnham and Sweeney, 1989; Sweeney andBurnham, 1990), based on the rate of cracking of the most impor-tant volatile products from vitrinite. The generation of these com-pounds is described by a first order Arrhenius equation and theprocedure follows the basic work of Karweil (1956) and improve-ments by Tissot and Espitalié (1975). The use of both of the chem-istry based VR equations is limited for high pressure conditionsbecause they do not consider the important pressure effect on VRdemonstrated in this study. It is of interest to compare the wellknown kinetic model of VR evolution EASY%Ro with the experimen-tal VR obtained in this study at 400 �C. We calculate VR evolutionwith time at 400 �C with EASY%Ro and plot it in the experimentalVR(P, 400 �C, t) versus t diagrams (Fig. 11). The rate model EASY%Ro

of Sweeney and Burnham (1990) provides VR that are higher thanthe 2 kbar experimental data and lower than the 20 kbar runs. Thedisparities between the model and the laboratory maturation areless at 10 kbar: VR calculated with EASY%Ro are slightly lower thanthe experimental VR. It is obvious that the upper temperature limitis reached at 400 �C for the use of EASY%Ro. This argues for a strictuse of EASY%Ro for temperature T� 400 �C. In addition, the dispar-ities between modeled and experimental maturation change withincreasing pressure. It shows the importance to include pressureas a parameter controlling the maturation in kinetic model of VRevolution. We believe that our kinetic experiments on vitrinitematuration may aid in model (e.g., EASY%Ro) improvement. How-ever, the phenol kinetic and the popular EASY%Ro methods are use-ful tools to calibrate and model VR at very low temperature andwhen the pressure effects on VR evolution rates can be neglected,i.e., at very low pressure conditions.

This discussion points out several limitations in the alreadyexisting VR equations and demonstrates the strength of experi-mentally derived empirical VR rate equation to model VR evolution.

5. Summary

The experimental results demonstrate that VR increases withheating time at 400 �C and at each investigated pressure. Despiterapid initial kinetics, a deceleration of VR increase with time takesplace at each pressure. A variation in pressure effects on VR increasekinetics is found. When VR < 1.44%, increasing pressure decreasesthe rate of VR increase and hence retards the initial VR enhance-ment. Consequently, the lower pressure, the higher are the initialVR magnitude and evolution kinetics. Nevertheless, the retardingeffect of pressure on VR increase diminishes with enhancing VR.However, a VR of 1.44% is rapidly attained (only a few hours) at400 �C. Therefore, the retardation of VR increase is insignificantfor geological maturation at 400 �C. When VR > 1.44%, increasingpressure reduces the deceleration of VR enhancement with time

and thus results in a larger VR increase with time at 400 �C. Obvi-ously, heating time and pressure promote VR increase and the mat-uration of Type III organic material at 400 �C. In addition, Type IIIorganic matter maturation is shown to rapidly occur in a dry con-fined system and does not require added water. Finally, a strong ef-fect of the experimental heat-up on VR is identified and quantified,even on experiments of very short duration. This information isimportant because the experimental heat-up effect must be cor-rected in kinetic analysis.

The evolution of vitrinite reflectance with time and pressureat 400 �C from an initial VR value of 0% is accurately describedby our new power law rate equation VR(P, 400 �C, t) =(k(P, 400 �C) t)n(P, 400 �C), where the exponent n(P, 400 �C) in-creases linearly with pressure and the rate constant k(P, 400 �C)that obeys a power law equation with pressure, increases withpressure. This VR evolution rate equation with its associated powerlaw exponent n(P, 400 �C) and rate constant k(P, 400 �C) accountsfor our experimental observations. In particular, this equation de-scribes the expected increase in VR with time inasmuch as n(P,400 �C) > 0. Nevertheless, this equation calls for a deceleration ofVR increase with time because n(P, 400 �C) < 1. Furthermore, theVR power law rate equation shows the observed pressure effectson VR evolution kinetics. Increasing pressure results in the lesserdeceleration of VR enhancement with time because n(P, 400 �C) in-creases with pressure. With increasing pressure, the power lawrate equation displays the initial VR increase retardation whenVR < 1.44% and the larger VR increase with time when VR > 1.44%.

We regard our kinetic formulation as a step toward a generalequation describing VR evolution as a function of time, pressureand temperature for Type III organic matter. Such VR rate equationis empirical and based on VR measured after experimental matura-tion of vitrinite under various pressure, temperature and heatingtime conditions. Our rate equation is not based on chemical kinet-ics because the chemical reactions in organic matter/vitrinite mat-uration are complex. We show the potential of the power lawformalism to model VR from any starting VR and for complex meta-morphic and heating time histories by making explicit how to usesuch a kinetic equation. The power law formalism is a simple andfast algorithm to simulate VR–P–T–t evolution. This is an advantageto model large-scale sedimentary basins and metamorphic terr-anes. Kinetic models that do not consider the effects of effectiveheating time, pressure and experimental heat-up to reach the de-sired run temperature may not accurately account for the evolu-tion of vitrinite reflectance in natural systems. Despite theseadvances, significant insights into VR evolution kinetics mayemerge through future experimental studies at different tempera-tures or/and in wet (water added) confined systems.

Acknowledgements

This research was supported by the Deutsche Forschungsgeme-inschaft (DFG) Grant BA 3527/1-1. We thank T. Kautz for help inthe high-pressure lab, V. Bullatov for technical discussions duringmachining of the piston-cylinder assemblies, W. Püttmann for ana-lyzing the chemistry of the xylite sample, M. Dolezych for supply-ing the original xylite and S. Weinbruch for a check of themanuscript. The manuscript greatly benefited from detailed com-ments by A. Burnham, R. Hill and an anonymous reviewer. R. Littkeprovided useful reviews on an earlier draft of this paper.

Associate Editor—Ken Peters

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