The Constraints of the Laws of Thermodynamics upon the Evolution of Hydrocarbons: The Prohibition of Hydrocarbon Genesis at Low Pressures.

 

J. F. Kenney

Joint Institute of The Physics of the Earth - Russian Academy of Sciences

Gas Resources Corporation, 11811 North Freeway, Houston, TX 77060, U.S.A.

I. K. Karpov

Institute of Geochemistry - Russian Academy of Sciences

Favorskii Street 1a, Irkutsk,  664.033 RUSSIA

Ac. Ye. F. Shnyukov

National Academy of Sciences of Ukraine

Khmelnitskogo Street 15 B, 01650 Kiev, Ukraine

V. A. Krayushkin

I. I. Chebanenko

V. P. Klochko

Institute of Geological Sciences - National Academy of Sciences of UKRAINE

O. Gonchara Street 55-B, 01054 Kiev, Ukraine

 

 

          This first article dealing with the general subject of the modern Russian-Ukrainian theory of abyssal, abiotic petroleum origins does not itself involve specifically that body of knowledge.  This article discusses the reasons which led physicists, chemists, thermodynamicists, and chemical, mechanical, and petroleum engineers to reject, already by the last quarter of the nineteenth century, the hypothesis that highly-reduced hydrocarbon molecules of high chemical potentials might somehow evolve spontaneously from highly-oxidized biological molecules of low chemical potentials, and reviews briefly the fundamental scientific reasons for the failure of the 18th-century hypothesis1 of a biological origin of petroleum.

          A fundamental attribute of modern Russian petroleum science is that it conforms to the general, fundamental laws of physics and chemistry.  Although such constraint may seem an obvious requisite for any scientific assertion, the 18th-century hypothesis that petroleum might somehow evolve spontaneously from biological detritus in the near-surface depths of the Earth stands, contrarily, in glaring violation of the most fundamental, and irrevocable, laws of nature:  the second law of thermodynamics.

 

          The second law of thermodynamics is a statement of irreversibility, and is an acknowledgement that spontaneous physical processes “go only one way.” Such property of the natural world is commonly and inevitably experienced in day-to-day life.  Such common, irreversible phenomena as heat flow, diffusion, and chemical reactions are constantly observed.

          When any two bodies at different temperatures are placed in contact, and no other action is taken upon them, heat flows from the hotter body to the colder, until such time as their respective temperatures become equal throughout their volumes;  at which time the flow of heat ceases;  and the process never reverses, so as to return the initially hotter body to any temperature higher (and the initially colder body, lower) than the final equilibrium temperature.

          Similarly, when two miscible fluids are placed in the same volume (such as a drop of cream in a coffee cup), and no other action is taken upon them, each fluid diffuses throughout the other, until such time as their respective densities become equally uniform throughout the volume;  at which time the diffusive flow ceases;  and the process never reverses, so as to return either fluid to any local density higher than the final equilibrium one.

          Likewise for chemical processes, when any two chemical species capable of reacting (reagents) are placed in contact, and no other action is taken upon them, chemical reaction proceeds, until such time as the reagents have reached their equilibrium chemical state;  at which time the reaction ceases;  and the process never reverses, so as to return the chemical products to the state of the initial reagents.

          The scientific principle which subsumes all of these intuitively obvious processes is the second law of thermodynamics.  When the second law of thermodynamics is expressed in its mathematical (and general) form, it may be used directly to predict whether any hypothesized chemical reaction will proceed, at any temperature or pressure.

 

1.       The second law of thermodynamics; thermodynamic stability; and the evolution of multicomponent systems.     

          The second law of thermodynamics was first enunciated by Clausius,2, 3 who defined the physical entity named entropy, S, and specified that its change, for every physical transformation, dS, is given as:

.                                                                                                 (1)

In equation (1), dQ represents the quantity of heat transferred between the system and its external world;  and dQ'/T represents the quantity of entropy produced internally by the system during the course of the transformation.  The second law of thermodynamics requires that this latter quantity, the entropy produced internally in course of any spontaneous transformation, be positive:

.                                                                                            (2)

The entity dQ', has been further refined by De Donder4, 5, such that

 

                                                                                                   (3)

 

in which

.                                                               (4)

In equation (4), μi,ρ and νi,ρ are, respectively, the chemical potential and stoichiometric coefficients of the i-th component in the ρ-th reaction;  α designates the respective phase, and dξ represents the differential of the variable of extent, ξ, which describes the evolution of the system.  The chemical potentials, μi, represent the amount of work which must be done upon a system to add another particle (or mole) of the i-th specie while all other variables describing the system are held fixed.

          Because the second law requires that the internal production of entropy be always positive, the direction of evolution of any system must always obey the inequality,

.              (5)

In equation (5), Fk and dXk are, respectively, general thermodynamic forces and flows.6, 7 The sum of the products of the thermodynamic Affinities and the differential of the variables of extent, dξρ, is always non-negative; and the circumstance for which the change of internal entropy is zero defines equilibrium, from which there is no spontaneous evolution.  The inequality (5) expresses the irreversibility of spontaneous transitions, and states: first, that for a spontaneous evolution of a system from any state, A, to any other state, B, the free enthalpy of state B must be less than that of state A; and that at no point between the two may the free enthalpy be greater than that of state A, or less than that of state B.  The rightmost expression in (5) states further that, for any circumstance for which the Affinity does not vanish, there exists a generalized thermodynamic force which drives the system toward equilibrium.

 

          The mathematical entity defined as the thermodynamic Affinity, A({μi}), is central to any analysis of chemical stability and determines the direction of evolution of a system in accordance with the second law of thermodynamics, as expressed by De Donder’s inequality.  Thus, the evolution of a chemically reactive, multicomponent system may be determined at any temperature, pressure, or composition whenever the chemical potentials of its components are known. To ascertain the thermodynamic regime of the spontaneous evolution of hydrocarbons their chemical potentials must be determined.

 

 

2.       The thermodynamic energy spectrum of the normal alkanes and the Hydrogen-Carbon  [H-C] system.

Fig. 1 Thermodynamic spectrum of elemental carbon @ STP.

          Consideration of the thermodynamic energy spectrum of the hydrogen-carbon [H-C] system must begin properly with its simplest elemental subset:  the chemical potentials of the elements carbon and hydrogen.  The chemical potentials of the H-C system will be reviewed first at standard temperature and pressure [STP: T = 298.15 K, p = 1 bar].  At STP, carbon can exist either as graphite or diamond, hydrogen only as a diatomic gas.  The respective chemical potentials of molecular hydrogen and graphite are  both identically zero at STP;  that of diamond is 0.685 kcal.  The simple spectrum of the elemental carbon system at STP is shown graphically in Fig. 1.  The higher chemical potential of diamond establishes that it is thermodynamically unstable at STP, and that graphite will never evolve spontaneously into diamond at either STP or any temperature in a regime of pressure for which diamond possesses a higher chemical potential.  The superficial appearance of stability of diamond at low temperatures is attributable to its very slow rate of transition to the graphite phase, a circumstance which enables diamond to manifest long-term kinetic stability in what is in fact only a  metastable state.

 

          The most common compounds of the H-C system are the normal alkanes.  The first and simplest member of the normal alkane system is methane, a tetrahedral molecule;  the second, ethane, C2H6, is a dumbbell-type molecule, the simplest of the chain-like configuration.  With propane, C3H8, and the following members of the n-alkane series, the molecules assume the geometric configuration of chain molecules.  As chain molecules, their chemical and thermodynamic behavior manifest the property that these compounds interact essentially as units of a chain. Such behavior is apparent in, for example, Brønsted’s principle of congruence,8 which predicts that the thermodynamic properties of a mixture of, say, n-butane and n-octane, will be closely similar to one of n-pentane and n-heptane, - e.g., for the excess volume of the mixture, vex(n-C4H10+n-C8H18)  vex(n-C5H12+ C7H16), - and in the principle of corresponding states for liquids consisting of chain molecules,9 which properties stimulated the first enunciation of the Hard Chain Theory by Prigogine in 1957.10  The thermodynamic energy spectrum of the chemical potentials of the normal alkane system for the compounds methane, CH4, through C20H42, is shown graphically at standard temperature and pressure in Fig  2.  The spectrum of chemical potentials of the normal alkane system is remarkable for both its characteristic increase with degree of polymerization as well as its linear, and almost constant, magnitude of such

increase with carbon number.  With increasing polymerization, the alkane molecules manifest increased chemical potential of very approximately 2.2 kcal per added carbon atom, or CH2 unit. 

Fig  2 The chemical potentials of the n-alkane system at STP.11  (Note the chemical potentials of diamond and graphite.)

(The respective chemical potentials of diamond and graphite are shown also in Fig  2;  the relative difference of the chemical potentials of those phases of elemental carbon are to be compared to the considerably greater differences of the chemical potentials of the n-alkanes.)

          There exist also the branched isomers of the n-alkanes which vary from molecules involving a single branch, such as isobutane, to ones with several “branches”, such as the form of “octane” designated 2-4-4-isopentane, and the unusual form of pentane designated 2-2-dimethylpropane (tetramethylmethane), C(CH3)4. The chemical potentials of the simple branched isomers differ from that of the normal configuration by only a few percent, typically 2-4%.

          It deserves special note that the increase in chemical potential with increased polymerization contrasts strongly with the thermodynamic spectrum of the highly oxidized, biotic carbon (“organic”) compounds of the H-C-O system, which manifest consistently decreasing chemical potentials with increasing polymerization.  This latter property allows the high degree of polymerization and complexity of the biotic compounds.

          The chain compounds of the H-C system that possess double or triple carbon-carbon bonds are designated, respectively, the n-alkene and n-alkyne series.  The alkenes have the general chemical formula, CnH2n, the alkynes, CnH2n-2.  The thermodynamic energy spectrums of chemical potentials of the n-alkene and n-alkyne series are shown in Fig. 4, together with that for the n-alkane series.  (The scale for energy has necessarily been decreased, and the chemical potentials of graphite and diamond do not show on Fig. 4.  It may be noted in Fig. 4 that, after the second member of both the alkene and alkyne series, the spectra of chemical potentials of both are identically linear which carbon number.  As for the n-alkane series, this property obtains from the nature of the polymerization process that involves substitution of two carbon-carbon bonds for a one with insertion of a CH2 radical.  A chain hydrocarbon compound can possess more than one double carbon-carbon bond;  and the chemical potential of such a compound would be very closely that of the n-alkene of the same carbon number plus the difference in chemical potential between that compound and the n-alkane of the same carbon number.  The same property holds for the compounds with more than one triple carbon-carbon bond.  Very few alkenes are found in natural petroleum, and no alkynes.

          In addition to the chain compounds, the H-C system possesses also many cyclic compounds: cyclic pentanes, hexanes, benzenes, and combinations of those compounds;  all of which are observed in natural petroleum.  The thermodynamic energy spectra of the naturally occurring compounds of the H-C system are shown graphically in Fig. 3, in which may be observed that the chemical potentials of combinations of the cyclic compounds with other chain elements share the linear property of the n-alkanes.

 

          When a hydrogen atom in a hydrocarbon compound is removed and replaced with a hydroxyl radical, OH, the chemical potential is decreased by approximately 32 kcal.  The resulting compound is a simple alcohol, possessing a chemical potential lower than that of methane, the hydrocarbon of lowest chemical potential, by 20-40 kcal.  Thus methane, in the presence of oxygen, can transform spontaneously into methanol, or ethane into ethanol.

  

Fig. 3 Thermodynamic energy spectrum of the naturally-occurring hydrocarbons.

        For example, the cyclic hydrocarbon, cyclohexane C6H12, is a typical volatile liquid hydrocarbon found in natural petroleum which possesses a chemical potential at STP of approximately 6.37 kcal/mol, shown schematically in Fig. 5.  When a hydrogen atom is removed from cyclohexane and replaced with an OH radical, the resulting molecule, cyclohexanol, is a typical, cyclic alcohol, which possesses a chemical potential at STP of approximately -34.30 kcal/mol.  When a second hydrogen atom is removed from cyclohexane and replaced with an OH radical, the resulting molecule is a dihydric alcohol, with properties similar to glycol;  and when a third hydrogen atom is removed and replaced with still another OH radical, the resulting molecule is a trihydric alcohol with properties similar to glycerin.  When one of the hydrogen atoms has been removed from each of the carbon positions and replaced by an OH radical, the resulting molecule, C6H12O6, is a simple, cyclic carbohydrate, of the sugar family, meso-inositol, alternately called “meat sugar,” found in both the animal and plant kingdoms.  This compound is shown schematically in Fig. 6 and possesses a chemical potential at STP of approximately -217.1 kcal/mol.  At each step of the process, and each replacement of a hydrogen atom with an OH radical, the chemical potential of the molecule decreases by approximately 34-36 kcal/mol.  Thus, such oxidation processes, by which a reduced hydrocarbon molecule of high chemical potential transforms into an oxidized one of low chemical potential, are in accordance with the second law, and can proceed.  However, the reverse process, involving the replacement of the OH radical with hydrogen to produce a reduced, hydrocarbon molecule of high chemical potential from an oxidized one of low chemical potential, would violate the second law, and does not.

          Examination of the H-C-O system of oxidized carbon compounds establishes that the chemical potentials of almost all biotic compounds lie far below that of methane, the least energetic of the reduced hydrocarbon compounds, typically by several hundred kcal/mol. Although there exist biotic molecules of unusually high chemical potential, such as β-carotene (C40H56), vitamin-D (C38H44O), and some of the pheromone hormones, such compounds are relatively rare by abundance. They are produced by biological systems only when the producing entity is alive, and at formidable metabolic cost to the producing entity; and the production of such compounds ceases with the death of the entity. Such compounds are not decomposition products of other biotic compounds, and are labile and themselves decompose rapidly. For these foregoing reasons, such compounds cannot be considered relevant to the subject of the origin of natural petroleum.

 

          These properties of both the hydrogen-carbon [H-C] and the hydrogen-carbon-oxygen [H-C-O] systems are represented graphically in Fig. 7.  Particularly to be noted in Fig. 7 is the break (of 150 kcal) in the left ordinate on which are given the chemical potentials of the compounds.  The chemical potential of the highest of the biotic carbohydrate compounds lies some 200 kcal below

that of the least energetic of the hydrocarbon compounds, methane.  Such other biological molecules as proteins and lipids are not shown on Fig. 7;  their chemical potentials lie as low, or (usually) much lower even than those of the carbohydrates.

 

 

Fig. 4 Thermodynamic energy spectrum of the straight-chain n-alkanes, n-alkenes, and n-alkynes.

          These properties of the thermodynamic energy spectrum of the H-C and H-C-O systems, together with the constraints of the second law, De Donder’s inequality, (2), determine three crucial properties of natural petroleum:

 

(1.)    The H-C system which constitutes natural petroleum is a metastable one in a very non-equilibrium state.  At low pressures, all heavier hydrocarbon molecules are thermodynamically unstable against decomposition into methane and carbon, - as is similarly diamond into graphite.

(2.)    Methane does not polymerize into heavy hydrocarbon molecules at low pressures, at any temperature.  Contrarily, increasing temperature (at low pressures) must increase the rate of decomposition of heavier hydrocarbons into methane and carbon.

(3.)    Any hydrocarbon compound generated at low pressures, heavier than methane, would be unstable and driven to the stable equilibrium state of methane and carbon.

 

          The first two conclusions have been amply demonstrated by a century of refinery engineering practice. The third conclusion has withstood the test of many attempts in laboratories to convert biotic molecules into hydrocarbons heavier than methane.

 

          There are two generic chemical processes involving the C-H-O system which deserve specific consideration: the “charcoal burner’s reaction,” and the “bean-eater’s reaction,”  Both describe limited reactions by which a highly oxidized biotic molecule can react to produce elemental carbon or methane when “carried” by a more thorough oxidation process. In both the following examples, the simple carbohydrate, sugar C6H12O6, is used as a typical biotic reagent; the same reasoning and results hold also for any of the highly-oxidized biotic compounds.

          The “charcoal burner’s reaction” is:

                                                                                 (6)

The chemical potential of water vapor at STP is -54.636 kcal/mol. The thermodynamic Affinity for the “charcoal burner’s reaction,” (6), to produce amorphous carbon, or graphite, is 109.10 kcal. Therefore, the genesis of coal from biological detritus in an oxygen-poor environment is permitted by the second law.  However, the thermodynamic Affinity for the “charcoal burner’s reaction” to produce diamond is 105.02 kcal, which quantity is also positive, and therefore not immediately prohibited by the second law as expressed solely by de Donder’s inequality, the first of equations (5).  Nonetheless, no charcoal burner

Fig. 5 c-hexane, C6H12; μo = 6.37 kcal/mol.

Fig. 6 Simple cyclic sugar, C6H12O6, meso-inositol (meat sugar); μo  = -217.1 kcal/mol.

ever scrabbles through his ashes hoping to find diamonds.  Such reasonable behavior demonstrates an effective appreciation of the dictates of the second law as expressed by the second of equations (5).  In this case, the generalized force is the difference in thermodynamic Affinity between the reactions for graphite and diamond, respectively, δF = δA/T, which, in the regime of temperatures and pressures of the near-surface crust of the Earth, assures always the genesis of graphite, never diamond.  Similarly, for reactions involving hydrocarbons heavier than methane, the same generalized force, δA/T, always drives the system toward the state of lowest free enthalpy, i.e., methane plus free carbon.

          The “bean-eater’s reaction” is:

                                                                              (7)

The chemical potentials at STP for the simple carbohydrate C6H12O6, methane, and carbon dioxide are, respectively in kcal/mol: -218.720; -12.130; and -94.260. The thermodynamic Affinity for this reaction is accordingly 100.42 kcal/mol, which is positive and therefore permitted by the second law. Indeed, reactions of the type (7) are typical of those by which methane is produced in swamps, sewers, and the bowels of herbivores. However, no such process ever produces heavier hydrocarbons, for such process would involve effectively a reaction of low-pressure methane polymerization. The effective prohibition of such a reaction can be understood by considering the “charcoal burner’s reaction.”         For both the production of methane and the decomposition of heavier hydrocarbons, there exist hydrocarbon metabolizing microbes which exist by exploiting the differences in the chemical potentials of the hydrocarbon compounds and elemental carbon, water, and carbon dioxide.  The metabolic processes of such microbes involves several intermediate steps, instead of the single-process step described in equations (6) and (7);  however the final differences of the thermodynamic Affinity remains the same, as does also the thermodynamic argument, above.

Fig. 7 Thermodynamic energy spectrum of the naturally occurring hydrocarbons and representative alcohols and biotic carbohydrates.  (Note the scale break at -‑50 kcal/mol.)

          The “octane-enhanced bean-eater’s reaction” is:  C6H12O6  1/8C8H18 +7/8H2 + 2CH4 + 3CO2.  Since the chemical potential at STP of n-octane is 4.290 kcal/mol, and that of molecular hydrogen is zero, the thermodynamic Affinity for the “octane-enhanced bean-eater’s reaction” is = (100.42 - 12.130 - 4.290/8) = 87.70 kcal/mol, still positive and thereby not prohibited outright by the constraints of De Donder’s inequality. However, no biochemical investigation has ever observed a molecule of any hydrocarbon heavier than methane resulting from the decomposition of biological detritus. After a meal of, e.g., Boston baked beans, one does experience biogenic methane, - but not “biogenic” octane. No such process produces heavier hydrocarbons, for such process would involve effectively a reaction of low-pressure methane polymerization, similarly as the effective prohibition of the evolution of diamonds by the “charcoal burner’s reaction.”

 

         Common industrial techniques, by which useful intermediate products can be obtained by controlling the reaction process, involve processes similar to the “octane-enhanced bean-eater’s reaction.”  The Fischer-Tropsch synthesis process uses reactions essentially identical to the “octane-enhanced bean-eater’s reaction” to generate liquid petroleum fuels from the combustion of coal, wood, or other biotic matter.  However, the highly-controlled, industrial Fischer-Tropsch process does not produce, uncontrolled and spontaneously, the commonly observed, large accumulations of natural petroleum.

 

          Not only does the hypothesis of a biological origin of petroleum assert processes which are glaringly in contradiction to the second law of thermodynamics, but such stands in violation also of the fundamental law of the conservation of mass for chemical processes.  Even if somehow the evolution of highly-reduced hydrocarbon molecules of high chemical potentials might somehow (miraculously) evolve from highly-oxidized biological molecules of low chemical potentials, the law of the conservation of mass would require that, for every ton of oil so generated, 8-10 tons of coal would necessarily also be generated, and likewise for every ton of natural gas, 12-15 tons of coal.12-14  Such deposits of coal are not observed with deposits of natural petroleum.

 

          The foregoing properties of natural petroleum, and the prohibition by the second law of thermodynamics of its spontaneous genesis from highly-oxidized biological molecules of low chemical potentials, were clearly understood in the second half of the 19th century by physicists, chemists and thermodynamicists, such as Berthelot, Sokolov, Biasson, and Mendeleev. However, the problem of how, and in what regime of temperature and pressure, do hydrogen and carbon combine to form the particular H-C system manifested by natural petroleum, remained. The resolution of this problem had to wait a century for the development of modern atomic and molecular theory, quantum statistical mechanics, and many-body theory.  This question has now been resolved theoretically by determination of the chemical potentials and the thermodynamic Affinity of the H-C system, using modern quantum statistical mechanics, and has also now been demonstrated experimentally with specially designed high-pressure apparatus, and is described in the following articles.

 

 

1        M. V. Lomonosov, Slovo o reshdinii metallov ot tryaseniya zemli, Akadimii Nauk, St. Petersburg, 1757.

2        R. J. E. Clausius, The Mechanical Theory of Heat, Berlin, 1850.

3        R. J. E. Clausius, "The Mechanical Theory of Heat", Phil. Mag., 1862, xxiv, 201.

4        T. De Donder, L'Affinité, Gautier-Villars, Paris, 1936.

5        T. De Donder and P. Van Rysselberghe, The Thermodynamic Theory of Affinity, Stanford University Press, Menlo Park, 1936.

6        I. Prigogine and R. Defay, Chemical Thermodynamics, Longmans, London, 1954.

7        D. Kondepudi and I. Prigogine, Modern Thermodynamics:  From Heat Engines to Dissipative Structures, John Wiley & Sons, New York, 1998.

8        J. N. Bronsted and J. Koefoed, J. Kgl. Danske, Vedenskab Selskab, Mat.-Phys. Medd., 1946, 22, 1.

9        J. Hijmans, "Phenomenological formulation of the principle of corresponding states for liquids consisting of chain molecules", Physica, 1961, 27, 433-447.

10      I. Prigogine, A. Bellemans and C. J. Naar-Colin, "Theorem of corresponding states for polymers", J. Chem. Phys., 1957, 26, 751.

11      U. S. Bureau of Standards, Selected properties of hydrocarbons, A.P.I. Project 41, 1946-1952.

12      A. S. Eigenson, "On quantitative study of the formation of technogenic and natural hydrocarbons using methods of mathematical modeling", Khimiya i Teknologiya Topliv i Masel, 1990, 12, 19-254.

13      A. S. Eigenson, "On quantitative study of the formation of technogenic and natural hydrocarbons using methods of mathematical modeling", Khimiya i Teknologiya Topliv i Masel, 1991, 5, 19-26.

14      A. S. Eigenson, "Quantitative study of some notions about catagenesis which is a main stage of biogenic oil-gas formation", Khimiya i Teknologiya Topliv i Masel, 1996, 6, 31-36.