Abstract
Determining oil migration distances from source rocks to reservoirs can greatly help in the search for new petroleum accumulations. Concentrations and ratios of polar organic compounds are known to change due to preferential sorption of these compounds in migrating oils onto immobile mineral surfaces. However, these compounds cannot be directly used as proxies for oil migration distances because of the influence of source variability. Here we show that for each source facies, the ratio of the concentration of a select polar organic compound to its initial concentration at a reference point is independent of source variability and correlates solely with migration distance from source rock to reservoir. Case studies serve to demonstrate that this new index provides a valid solution for determining source-reservoir distance and could lead to many applications in fundamental and applied petroleum geoscience studies.
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Introduction
Petroleum is generated via thermal alteration of buried organic matter in source rocks, followed by oil expulsion (primary migration) out of those source rocks. Petroleum accumulations are formed mainly via subsequent secondary migration from source rocks through carrier beds to traps. Information about the directions, pathways and distances of secondary petroleum migration is required in the search for new petroleum resources. However, secondary petroleum migration still remains the least understood of the processes involved in petroleum accumulation. Because fractionation of polar organic molecules can result from preferential sorption of these compounds in migrating oils onto immobile mineral surfaces or through partitioning into formation water, molecular indices that are correlated solely with the absolute or relative migration distances migrated by oils have been sought for decades1,2, but with limited success.
Nitrogen-, sulfur- and oxygen-containing compounds exhibit strong sorption on minerals and/or high solubility in water due to their polarities and thus variations in the distribution of these molecules are used to study oil migration processes3,4. However, those compounds with high solubility in water such as alkylphenols can be easily affected by water saturation, water washing and injection for enhancement of oil production and are sensitive to any oil-water interactions in the subsurface environment5. Concentrations and ratios of carbazoles (nitrogen-containing compounds) were previously used as proxies of secondary migration distances2,6,7,8,9,10,11,12,13,14, based on their low solubility in water15. However, recent studies show that these empirical indicators do not solely reflect migration-related fractionations and thus do not actually correlate with migration distance, because their concentrations and ratios can also be affected by variations in organic facies (such as marine, lacustrine, or terrigenous organics; anoxic or suboxic depositional environment; carbonate or shale lithology) and thermal maturation of source rocks as well as biodegradation of oils8,10,16,17,18,19,20. In addition, it appears that properties of migration systems, such as porosity, sorption coefficients, oil saturation and oil volume, may also influence the utility of these tracers4.
Among these influences, the biodegradation effect on carbazoles is negligible when biodegradation levels are less than 3 on the scale of Peters and Moldowan (1993)20,21. On the other hand, source input influences due to variations in source facies and maturity of organic matter, a parameter related to the maximum temperature experienced by source rocks at the time of oil expulsion, are significant and thus cannot be ignored8,10,16,17,19,22. The influence due to the variability of source facies can be minimized by grou** oils according to their source facies22. However, the maturity effect has been difficult to evaluate and impeded studies of secondary petroleum migration.
It is difficult, if not impossible, to find an oil component in nature that is independent of source input influences. Nevertheless, it is feasible to set up a secondary migration fractionation index (SMFI) that is independent of source input influences, reflects only migration-related fractionation and thus correlates directly with migration distance. Here, we advance the concept of SMFI as a reliable measure of migration fractionation and migration distances for a uniform migration system, where porosity, density of solids, sorption coefficients, migration velocity of oil and oil saturation are kept constant. More realistic migration systems with variable properties could be treated by dividing them into subsections with constant properties. The SMFI is defined as the ratio of the concentration of a large polar compound (heavier than 160 Dalton) with low concentration (e.g. carbazoles) to its initial concentration at a reference point for each source facies. In other words, the concentration of the large polar compound is actually a product of the initial concentration (controlled by source input influences) and the index that characterizes fractionation solely with secondary migration distance (see Equations (1, 4 and 5) in the methods section). Oil volume passing through a carrier bed or multiple charging events do not affect the validity of the ratio, when appropriate compounds with very low concentration in petroleum are selected as tracers (see for details in the multiple charging and oil volume section in the online Supplementary Information). This new SMFI is fully described in the methods section and mathematically derived in the Supplementary Information based on the mass balance principle and advection-reaction-dispersion theory.
We then apply and test the validity of the new index in the Ordos and Western Canada Sedimentary basins where both concentrations and ratios of carbazoles do not effectively reflect migration-related fractionations and thus the distances of secondary petroleum migration. The narrow, long, continuous and clay-rich sand body of the ** of oil and gas: a fundamental principle. AAPG Bulletin 38, 816–853 (1954)." href="/article/10.1038/srep02487#ref-CR23" id="ref-link-section-d109436831e619">23 of differential petroleum entrapment involving long distance migration along the reef trend in the up-dip direction. However, this theory is still being debated mainly because the empirical indicators do not show obvious migration fractionations for most oils along the reef trend. We demonstrate that our SMFI fits the actual data well and is a reliable odometer for the distance of secondary petroleum migration and we provide supporting evidence for the Gussow theory. The new index represents a significant step forward in petroleum geoscience as it can be used to reveal the distribution patterns of petroleum accumulations in sedimentary basins and to study theories on petroleum accumulation.
Results
We first tested the utility of the SMFI in the ** of oil and gas: a fundamental principle. AAPG Bulletin 38, 816–853 (1954)." href="/article/10.1038/srep02487#ref-CR23" id="ref-link-section-d109436831e1229">23 was derived from this trend but the convincing evidence for long distance migration along the trend has not yet been achieved. The Ro (equiv.) values of the oils along this trend vary from 0.68% to 0.86% (Supplementary Table S6). Sorption capabilities of carbazoles on minerals in carbonate reservoirs are very low compared to clastic reservoirs19. Therefore, benzocarbazoles were examined in these oils, as they are more easily adsorbed than alkylcarbazoles7. The results show that the maturity influence index of benzocarbazoles in the reef trend can reach 85.8% (Supplementary Table S7). The SMFIs and the ratio between SMFIs of benzocarbazoles, computed from the data in Supplementary Table S6, clearly show fractionations consistent with long distance migration along the reef trend in the up-dip direction with remarkably high correlation coefficients (Supplementary Figs. S5 and S6), providing basic evidence for the Gussow theory23. This is in good agreement with the results of oil-source correlation studies that include maturity information8,9. The various lines of evidence suggest that the Gussow theory is generally applicable. Further details are discussed in the Supplementary Information.
Discussion
Carbazoles not only have stronger sorption capabilities than nonpolar compounds but also hold information about their source inputs including source facies and maturity variations. Our study shows that small maturity variations of less than 0.2% in Ro (vitrinite reflectance) can contribute to over 50% of the concentration variations of alkyl- and benzocarbazoles. Given that the bulk of petroleum generation/expulsion occurs over the maturity range of 0.6% to 1.0% in Ro (ref. 2), the concentrations and ratios of carbazoles cannot be used directly as proxies for secondary petroleum migration distance in most basins where there exist significant influences of source variability. The secondary migration fractionation index, established in this paper, offers an effective solution to this problem and can serve as a distance indicator for secondary migration, as it eliminates the source maturity effect on oils grouped according to source facies and only reflects migration fractionation. This approach can be applied to other low concentration, large polar compounds with different sorption coefficients between isomers, although it is shown in this study for alkyl- and benzocarbazoles.
The ability of our index to reliably monitor secondary migration distances may lead to many applications in fundamental and applied petroleum geoscience studies. The index outlined here is a step towards correctly interpreting the behavior of low concentration, polar organic compounds in petroleum and thus it can help resolve many important questions in organic geochemistry and petroleum geology. Moreover, secondary petroleum migration in many basins around the world is poorly understood and yet the information about this process is most important for petroleum exploration2,8. Our index provides a new tool that can aid in the discovery of new resources via accurate assessment of the directions, pathways and distances of petroleum migration. The method established for calculation of the SMFI in this paper may or may not be universally applicable to oil accumulations with other than a simple linear geometry. The method for complex petroleum migration systems is the subject of future investigation.
Methods
Knowing the direction, pathway and distance of lateral secondary migration is essential in searching for new petroleum accumulations. In the following we develop a new methodology to track the distances of lateral secondary migration of oil through porous strata (such as sand bodies) or unconformities (erosional or non-depositional surfaces separating two strata of different ages).
From the mass balance principle, a general advection-reaction-dispersion equation40,41 (Supplementary Equation (S1)) can be established for secondary petroleum migration in a uni-dimensional pathway. The properties and types of pathways were studied by Yang et al. (2005)4. To investigate the source input influence, we focus here on a uniform migration system, in which the properties of the system, including porosity, density of solids, sorption coefficients, migration velocity of oil and oil saturation, are constant.
The general advection-reaction-dispersion equation can be simplified under the conditions below. When large polar compounds such as carbazoles are selected for a secondary migration study, molecular diffusion is insignificant42 and can be safely neglected4. Lateral migration is very slow, especially in cratonic basins such as the Ordos Basin. Precisely because of slow migration, the effect of mechanical dispersion (caused by differences in microscopic migration velocities on a pore scale) is smaller than that of molecular diffusion and thus can be omitted40. Therefore, dispersion including molecular diffusion and mechanical dispersion can be neglected (see discussions in paragraphs following Supplementary Equation (S1)). Partitioning between oil and water is neglected because adsorbable compounds with low solubilities in water must be selected for a secondary migration study. Secondary petroleum migration in carrier beds in the up-dip direction results in decreases in temperature and thus holds back or slows down the thermal evolution of oils if the basin does not subside substantially. In this scenario, we assume that only sorption occurs during secondary migration, to reveal migration fractionation. Thus, the general advection-reaction-dispersion equation reduces to advection-sorption equation (Supplementary Equation (S4)).
Sorption of carbazoles in migration systems can approach equilibrium on geological time scales4,43. In sorption equilibrium theory, the linear isotherm model (Supplementary Equation (S5)) is valid for the natural systems where concentrations of adsorbable compounds are low44. From the advection-sorption equation and linear isotherm model, we can derive the source-dependent migration model that describes how the concentration of a carbazole (or any other large, polar compounds present at trace concentration levels) varies with maturity and migration distances for any given type of source facies (see detailed deduction process from Supplementary Equations (S1) to (S21)):
where 
is the initial concentration of a carbazole at the filling point (i.e. starting point of secondary petroleum migration); 
(vitrinite reflectance) as a maturity variable is a function of time for a given type of source facies; both vitrinite reflectance (
) and its equivalent (
) quantitatively indicate the maturity levels with the same units and thus are represented by one variable (
) in the equations; 
and 
can also be expressed as 
and 
, respectively (refer to Supplementary Equations (S21 and S22)); 
, 
and 
are constants, which can be determined through non-linear regression analysis of Equation (1). The parameter 
is dictated by geochemical processes of hydrocarbon generation and fractionations in primary migration or migration before the reference point as defined in the next paragraph. It has units of concentration (μg/g). 
is a rate of change of initial concentration with Ro, defined in Supplementary Equation (S12). It is a dimensionless constant. If 
> 0, 
increases with 
; 
< 0, 
decreases with 
. Oils from different source facies will have different values of the constants 
and 
in Equation (1), reflecting different source input influences due to maturity variations among different source facies. The parameter 
is proportional to the ratio of the retardation factor of an adsorbable compound to oil migration velocity or is inversely proportional to migration velocity of the compound (Supplementary Equation (S20)). It has units of km−1. The value of 
is always negative when sorption occurs without any other reactions. Equation (1) indicates that low values of 
(i.e. large absolute value) cause rapid concentration decreases of the large polar compounds with migration distance if only the sorption effect is considered.
In the above, the filling point was used to define the absolute migration distance 
in the theoretical analysis (see details in the model section of the Supplementary Information). However, because it is difficult to determine the filling point in practice, a reference point is often used to determine the relative migration distance, which usually is located behind the filling point in a pathway and thus results in a 
representing the distance between the filling point and the reference point. Nonetheless, the relative migration distances can be directly used for estimating 
, 
and 
(without any correction for 
) via non-linear regression analysis of Equation (1), as 
and 
do not change with 
. Although 
varies with 
, the variable 
does not affect the study of the relative migration distance as both are directly correlative.
Equation (1) shows an exponential attenuation law style function with a variable initial concentration as a function of maturity. The derivation of Equation (1) is detailed from Supplementary Equations (S1) to (S22). This functional form is derived under the conditions of the linear isotherm sorption, very low dispersion and uniform pathways.
The initial concentration 
incorporates the source input information of a carbazole, its generation from a source rock and fractionation during primary migration (oil expulsion). 
was shown to vary steadily with maturity (
) in the range of 0.45–1.3% (ref. 8), so that most of the variation can be described by a quadratic equation that becomes linear over a narrow 
range such as 0.7–0.8% (Supplementary Table S3) in the **feng Oilfield (i.e. 
) (see Equation (S12) and its relevant discussion in the Supplementary Information).
As sorption equilibrium is achieved during secondary migration43 and the thermal evolution of the oil either stops or slows down after expulsion, provided that the basin does not subside substantially, the present concentrations of a carbazole and 
values of oils can be used to represent 
and 
values during secondary migration in Equation (1).
Our model (Equation (1)) was derived for uniform migration systems. More realistic migration systems with variable properties could be treated by dividing them into subsections with constant properties. To ensure the model validity, proper compounds must be selected that should satisfy the requirements of sufficiently low concentrations in oil, low solubilities in water and strong enough sorption capacity (see for further details in the multiple charging and oil volume section of the Supplementary Information). With these compounds, our model can also be applied to carrier systems with multiple charging, which is demonstrated via linearization of the Langmuir isotherm model (Supplementary Equations (S27–S32)). The geochemical conditions for valid application of the model and the selected compounds are: (1) the thermal evolution of oils expelled from source rocks ceases or the oil migrates in the up-dip direction without substantial basin subsidence after expulsion; (2) the primary migration fractionation index is nearly a constant; (3) the relationship between 
and the initial concentrations at the filling point or reference point is linear or can be described by a quadratic equation (see Supplementary Information for more details); and (4) oil biodegradation levels are <1 on the biodegradation scale of Peters and Moldowan (1993)21 or the effect of oil biodegradation is quantitatively removed.
In a previous study, the quantitative models on factors influencing the distribution of phenol and carbazole compounds4 did not address the issue of source input influences. In their pivotal model (Equation (33) in Yang et al. (2005)4), the geotracer concentration during secondary migration is constant and the same as the initial concentration at the filling point. This model (Equation (33) in Yang et al. (2005)4) can also be derived in our work as a special case (Supplementary Equation (S18)). In natural migration systems, however, the geotracer concentration during migration and initial concentration are all variable. Our new model (Equation (1)) is developed to address such complexities that are present in real systems.
Quantitative evaluation of source input influences, including organic source facies and maturity, is a necessary first step in order to eliminate source input influences. Here we begin with the total differential of Equation (1)
where 
represents concentration variation of a carbazole caused by maturity variation for oils from a given type of source facies and 
represents that caused by migration fractionation. The maturity influence index (
) for a given type of source facies is defined as
The migration fractionation contribution index (
) is equal to 100-
(%), based on Equations (2 and 3).
The maturity influence index quantitatively indicates the maturity influence in the source input information for a given type of source facies. Before using large polar compounds (e.g. carbazoles) to study secondary migration, the maturity influence index should be calculated to check whether the maturity influence is significant and thus must be removed. The case studies (see the results section) illustrate that when the maturity influence index is ≥5%, the distribution of concentrations and ratios of large polar compounds (e.g. carbazoles) do not solely reflect migration distance and thus the maturity influence must be removed.
To illustrate the net migration fractionation of a carbazole during secondary petroleum migration without maturity influence, we introduce the concept of a secondary migration fractionation index (
) for oils from a given type of source facies
Substitution of Equation (1) into (4) yields
Evidently, if a reference point is used instead of the filling point, Equations (3 and 5) are still applicable. Since the 
as defined above only reflects migration fractionation, it serves as an odometer for secondary migration in a uniform pathway. 
equals 100% at the reference point, which is defined as the model value. In the case of multi-source-facies, oils are first grouped according to their source facies. The 
, 
and 
are then estimated separately based on their respective source facies. This minimizes the influence arising from variations in source facies.
From Equation (5), we can derive
where 
is the geometric mean of 
and 
is the arithmetic mean of 
for one type of alkylcarbazoles. For example, 
represents the geometric mean of 
of N-H exposed dimethylcarbazoles (EDMCA).
From Equation (6), we can get further
where 
and 
are the geometric means of 
for two types of alkylcarbazoles, respectively. The 
indicates the arithmetic mean of 
of alkylcarbazoles of type one; 
, type two.
Similarly, the ratios of 
of different types of individual alkyl carbazoles can also help identify migration fractionation. From Equation (5), we can derive
where 
is the secondary migration fractionation index of an alkylcarbazole of type one; 
, type two. The 
represents 
of an alkylcarbazole of type one; 
, type two.
Evidently, 
, 
, 
and 
are all functions of migration distance 
, thus can all serve as odometers for secondary migration in a uniform pathway and can be used to identify migration fractionation and to further reveal migration directions or pathways. Both 
and 
decrease with migration distance when 
and 
are calculated from the compounds of the type with comparatively low sorption capacities or sorption coefficients. At the filling or reference point, 
equals 100% and both 
and 
equal 1.
The general approach of using our model and 
is summarized below:
-
1
Classify oils according to their source facies. For each type of source facies, conduct the following analyses;
-
2
Select a possible migration pathway and calculate the relative migration distance (as outlined in the results section for the distance calculation); conduct non-linear regression analysis of Equation (1) with the data of the relative migration distance, concentrations of geotracers and
, to derive the constants of 
, 
and 
in Equation (1); -
3
Conduct linear or polynomial regression analysis between
and migration distance 
, calculate 
and then compute maturity influence index (
) from values of 
, 
and 
, by using Equation (3); -
4
If maturity influence index is <5%, the maturity influence may be ignored. If it is ≥5%,
values of geotracers (such as carbazoles) are computed using Equation (4) with the data of concentrations, 
, 
and 
, as shown in the case of the **feng Oilfield; -
5
For carbazoles, calculate the geometric
means of exposed, partially exposed and shielded DMCAs (dimethyl carbazoles), ratios of geometric means of 
of N-H exposed/shielded, exposed/partially exposed, partially exposed/shielded DMCAs, the corresponding 
ratios of individual dimethyl carbazoles and 
ratio of benzo[a]/benzo[c]carbazole; -
6
Analyze the correlation of the
values, geometric means and ratios against relative migration distance; if a correlation is evident, identify migration fractions on the base of 
and the ratios calculated at the fifth step; if the correlation and migration fractions do not support a particular selected pathway being valid, other possible pathways should be investigated by going back to the second step; if migration fractionation exists, the migration pathway, distance and direction are confirmed further with comprehensive analysis of geological and geochemical data.
, to derive the constants of 
, 
and 
in 
and migration distance 
, calculate 
and then compute maturity influence index (
) from values of 
, 
and 
, by using 
values of geotracers (such as carbazoles) are computed using 
, 
and 
, as shown in the case of the **feng Oilfield; 
means of exposed, partially exposed and shielded DMCAs (dimethyl carbazoles), ratios of geometric means of 
of N-H exposed/shielded, exposed/partially exposed, partially exposed/shielded DMCAs, the corresponding 
ratios of individual dimethyl carbazoles and 
ratio of benzo[a]/benzo[c]carbazole; 
values, geometric means and ratios against relative migration distance; if a correlation is evident, identify migration fractions on the base of 
and the ratios calculated at the fifth step; if the correlation and migration fractions do not support a particular selected pathway being valid, other possible pathways should be investigated by going back to the second step; if migration fractionation exists, the migration pathway, distance and direction are confirmed further with comprehensive analysis of geological and geochemical data. In the case of large variations in maturity as shown in the Rimbey-Meadowbrook reef trend, a quadratic (
) needs to be added into the parentheses in Supplementary Equation (S12) and Equation (1) and Equations (2–4) are adjusted accordingly.
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Acknowledgements
We are grateful to Drs. Quan Shi and Minghui Wu who kindly provided assistance in oil sampling and analyses. Special thanks to Professor Deyi Xu who kindly checked the derivation of our model in the Supplementary Information and Professor Lloyd Snowdon for his English editing of the final version of the manuscript. We also thank the two anonymous reviewers and the journal editor for their many valuable and constructive comments and suggestions. This research was supported by China Sci-Tech Project of National Importance (No. 2011ZX05008-004-20), China National Major Science 973 Projects (Nos. 2003CB214608 and 2012CB214801), State Key Laboratory of Lithospheric Evolution, IGG-CAS Grant (No. Z201003) and Sinopec Sci-Tech Project (No. P11062).
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Authors and Affiliations
Contributions
L.Z. established the model and index, analyzed and processed the data and wrote the paper. M. L., Y. W. and Q.-Z. Y. analysed the data and wrote the paper. W.Z. analysed the data. All authors discussed the results and commented on the manuscript.