Article pubs.acs.org/EF
Quick Evaluation of Source Rock Kerogen Kinetics Using Hydrocarbon Pyrograms from Regular Rock-Eval Analysis Zhuoheng Chen,* Xiaojun Liu, and Chunqing Jiang
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Geological Survey of Canada, Calgary, Alberta T2L 2A7, Canada ABSTRACT: Source rock kinetics reflects kerogen reactivity that controls the onset and rate of hydrocarbon generation as well as the depth/temperature of oil and gas generation windows. Therefore, understanding source rock kinetics is critical to both quantitative resource modeling and identifying production “sweet spots”. The study of source rock kinetics requires special laboratory procedure and expertise, the cost of which limits research on specific source rock systems. For quantitative modeling of hydrocarbon generation, kinetic parameters are often adopted from an analogous source rock system available in published data sets or are automatically picked by basin modeling software based on kerogen type or depositional environment and facies. Recent studies (Peters, K. E.; Walters, C. C.; Mankiewicz, P. J. AAPG Bull. 2006, 90, 387−403) revealed that source rock kinetics may vary substantially, even for the same type of kerogen, because of compositional variation. Thus, source-rock-specific kerogen kinetics is more desirable for better characterization of the thermal transformational behavior. On the other hand, the requirements for information regarding the characteristics of source rock reactivity and hydrocarbon generation behavior are time-sensitive for supporting a business decision. Directly assessing reactivity and transformation behavior of source rock based on archived Rock-Eval data would allow for rapid and time-sensitive results to be obtained. This paper proposes a method that characterizes source rock kinetics using pyrograms of archived Rock-Eval analysis. Because the method uses existing Rock-Eval data directly, no new samples and laboratory experiments are required, thus providing a quick and cost-effective technique to determine simple kinetic parameters. The mathematical formulation of this numerical model is described herein, with applications showing the advantage and potential limitations.
1. INTRODUCTION Organic-rich shales are both source rock and reservoir in many shale gas/oil plays.2−4 Source rock evaluation is a key component in unconventional resource play assessment. Source rock kinetics, along with thermal maturity, controls the onset and rates of oil and gas generation. Thus, these are critical to both quantitative resource evaluation5 and identifying proliferous production zones.6,7 The traditional approach for determining oil generation kinetics uses laboratory pyrolysis at variable heating rates to mimic the hydrocarbon generation processes,8 allowing for the thermal energy required for hydrocarbon generation under differing geological conditions to be inferred. However, the requirements of special laboratory instruments, procedures, and expertise limits the number of source rock samples that can be analyzed for kerogen kinetics as a result of budgetary and time constraints. Results available in the public domain may also be problematic because they are not a direct reflection of a specific source rock or organofacies. For basin modeling or petroleum system analysis, the kinetic parameters are often “borrowed” from analogous source rock systems available in the literature, automatically picked by basin modeling software based on the kerogen type9 or depositional environment and facies. Recent studies suggest that numerical kinetic models derived from laboratory pyrolysis for particular source rock samples may result in appreciable errors when applied to source rock systems containing the same types of kerogen but deposited in different geological settings (e.g., marine type I versus lacustrine type I kerogen) as a result of differences in their activation energy spectra.1,10 Furthermore, publically available source rock kinetic parameters are largely restricted to the well-studied basins, Published 2017 by the American Chemical Society
further limiting the possible analogues useful for data interpretation and petroleum system modeling. Another challenge for the conventional kerogen kinetic approach is that immature source rock samples, required for laboratory pyrolysis analysis to derive the kinetic parameters, are not always available. An example of this is the Utica shale in Quebec, Canada, where the basin has undergone severe thermal alteration.11 Kerogen kinetics specific to a particular source rock unit is more desirable for characterizing the thermal transformational behavior of the source rocks. Because hydrocarbon resource exploration and development from shale reservoirs are capital-intensive, a quick and reliable play evaluation and early identification of “sweet spots” are essential for competitive advantages and success. In many cases, the requirements for information regarding the characteristics of source rock hydrocarbon generation are time-sensitive for business decisions. The capability of directly assessing the transformation behavior of target source rocks using archived Rock-Eval data would allow people to position themselves with a competitive advantage, because Rock-Eval results are available for almost any source rock system from sedimentary basins. A numerical method that extracts additional information from archived Rock-Eval hydrocarbon pyrograms to infer the kerogen hydrocarbon generation kinetics of a source rock system is described herein. The proposed method is validated first through a Rock-Eval sample with kinetic parameters from Received: June 28, 2016 Revised: October 7, 2016 Published: January 16, 2017 1832
DOI: 10.1021/acs.energyfuels.6b01569 Energy Fuels 2017, 31, 1832−1841
Energy & Fuels
Article
Figure 1. (a) Histogram showing the distribution of apparent activation energies, with each bar representing one particular group of kerogen with the same activation energy. The distribution of estimated activation energies are digitized from Dieckmann et al.,13 representing an immature source rock from the Devonian Duvernay Formation in WCSB. (b) Hydrocarbon generation curve (i.e., converted kerogen components) for each of the component groups. One bell-shaped curve represents a kerogen component group with a specific activation energy (a single bar in panel a). (c) Aggregated hydrocarbon generation rate by kerogen component groups (in panel a) from the highest to lowest apparent activation energy components, showing the remaining generation potentials (area under each bell-shaped curve) of the kerogen at particular maturity (represented by the corresponding temperature at the highest production rate for each bell-shaped curve) levels. The difference between any two bell-shaped curves represents the hydrocarbon generated in the temperature interval indicated by the two peak temperatures in the horizontal axis. The outmost bell curve represents the total hydrocarbon generation potential. (d) Cumulative product. estimated frequency factors and activation energies for each sample. Issler15 studied methods using single as well as variable frequency factors and found that the value of the estimated frequency factor depends largely upon the initial model condition. This study concluded that application of a single frequency factor to all activation energy components seems to be a reasonable approach because of the compensation effect of the two parameters. In our study, we use a single frequency factor optimized for the bulk kerogen conversion of each source rock sample. This is similar to the work by Braun and Burnham14 and slightly different from the approach taken by Waples,18 who used a fixed frequency factor for samples. Figure 1 demonstrates the assumptions and principles of our numerical model graphically. The histogram (Figure 1a) represents a kerogen compositional grouping based on apparent activation energy. The relative abundance of each kerogen group is represented by the height of each bar (frequency). The decomposition of each group proceeds independently as a first-order reaction. The product and conversional behavior of each group are represented by a single bellshaped curve in Figure 1b. The remaining hydrocarbon generation potential can be demonstrated by aggregating the products of each kerogen compositional groups from the highest activation energy to the lowest to mimic the Rock-Eval hydrocarbon pyrograms at various maturity levels (Figure 1c). The total conversion of kerogen to hydrocarbon is characterized by the cumulative product versus temperature in Figure 1d. Our numerical model can be described mathematically as follows: Let x be the concentration of convertible total organic carbon (TOC) in the source rock, and f(x) is a mathematical function of x describing the reaction of kerogen conversion to hydrocarbons. The kerogen thermal degradation in a source rock is approximated by a series of independent and parallel chemical reactions19
the literature. A case study using regular Rock-Eval data acquired on samples from the Devonian Duvernay shale system in the Western Canada Sedimentary Basin (WCSB) is used to demonstrate the application of the method in source rock evaluation.
2. METHODS 2.1. Numerical Model for Kerogen Conversion to Hydrocarbons. The proposed method attempts to reproduce numerically laboratory observations from Rock-Eval hydrocarbon pyrograms, so that the thermal stability and the conversion of kerogen can be calculated for data interpretation and hydrocarbon generation modeling. Hydrocarbon generation from kerogen in a source rock involves various chemical reactions. To make the mathematical model manageable but reasonably representative of the processes, we made assumptions and simplifications similar to those of Schaefer et al.12 and Dieckmann et al.:13 (a) kerogen thermal degradation in a source rock can be approximated by a series of first-order, independent, and parallel chemical reactions; (b) kerogen in a source rock is a mixture of maceral components, and each compositional group has distinctive thermal stabilities and transformational behavior that can be characterized by a specific activation energy (E) and frequency factor (A) in the Arrhenius equation; and (c) each group of kerogen components undergoes an independent and parallel first-order reaction, and its contribution to the overall production rate depends upon its abundance. Various algorithms based on the assumption of first-order and parallel reactions and using a single frequency factor and a distribution of activation energies have been proposed for studying source rock hydrocarbon generation kinetics.14−16 Li and Yue17 derived an algorithm using variable frequency factors and activation energies for individual parallel first-order reactions in a study of oil shale pyrolysis kinetics and showed a linear relationship between the logarithm of
dx = dt 1833
m
∑ ajkjf (xj) j=1
(1) DOI: 10.1021/acs.energyfuels.6b01569 Energy Fuels 2017, 31, 1832−1841
Energy & Fuels
Article
Figure 2. (a) Computer-generated pyrograms of an immature sample with known activation energy distribution shown in Figure 1a. (b) Comparison of estimated and original distributions of activation energy with different heating rates. where j represents the jth component of x, aj is the relative abundance of the jth component of x, kj is the reaction rate constant of the jth component, and m is the total number of kerogen compositional groups with ∑maj = 1 and x = ∑mxj. The absolute concentration is not important because all components are specified in terms of the relative abundance. The temperature dependency of the reaction rate constant kj is quantified using the Arrhenius equation
⎛ Ej ⎞ k j = A exp⎜ − ⎟ ⎝ RT ⎠
n
P(a) =
i=1
where A is the pre-exponential or frequency factor, Ej is the activation energy of the jth compositional group, R is the gas constant, and T is the absolute temperature. When a constant heating rate is assumed, defined by ξ = dT/dt, the rate of conversion becomes a function of the temperature. (3)
The reaction rate of kerogen conversion is then quantified as the sum of a series of parallel reactions of kerogen components in the source rock using the following expression:
dx = dT
m
∑ j=1
1 kj(T )f (xj) = ξ
m
∑ j=1
⎛ Ej ⎞ A exp⎜ − ⎟f (xj) ξ ⎝ RT ⎠
(4)
while the conversion of the jth compositional group can be approximated by the following equation:19
∫0
aj
1 dx = f (xj)
∫0
t
kj(T ) dt ≈
ART 2 ⎛⎜ 2RT ⎞⎟ ⎛ Ej ⎞ 1− exp⎜− ⎟ ⎜ ξEj ⎝ Ej ⎟⎠ ⎝ RT ⎠ (5)
The conversion of bulk kerogen to hydrocarbon is then a convolution of the decomposition rates of kerogen components with the activation energy aj.14 dx = dTi
m
∑ j=1
ARTi 2 ⎛ 2RTi ⎞ ⎛ Ej ⎞ ⎜⎜1 − ⎟exp⎜− ⎟aj ξEj ⎝ Ej ⎟⎠ ⎝ RTi 2 ⎠
i = 1, 2, ..., n , and j = 1, 2, ..., m
⎝ dTi
−
2 m dx ⎞ ⎟ + α ∑ (aj − aapr)2 dTio ⎠ j=1
(7)
where dx/dTi and dx/dTio denote observed and computed rates, respectively, and aj and aapr are observed and computed abundances, respectively. Parameter α is a weight for balancing the two terms in eq 7. The problem in estimating the relative abundance of kerogen components in fixed groups in terms of activation energy and frequency factor in eq 7 is treated as an optimization problem, which can be solved by any gradient-type technique. In our study, the regularized conjugate gradient (RCG) method is employed for estimating the unknown parameters. For mathematical details, the reader is referred to the work of Zhdanov.20 The numerical model and mathematical solution of this method are presented in the Appendix. 2.2. Rock-Eval Analysis of Source Rock Samples. All RockEval results on source rock samples were generated at the Geological Survey of Canada using the Rock-Eval 6 instrument of Vinci Technologies that can produce a TOC value. A finely powdered ( 0
6. CONCLUSION We proposed a method that uses pyrograms from regular RockEval analysis for calculating source rock kinetics. The method fits kerogen pyrolysis (S2) curves to a numerical model of kerogen thermal degradation reactions; thus, the transformation behavior of the remaining kerogen can be examined. The kinetic properties derived from this method can be used as input parameters for numerical modeling of hydrocarbon generation or integrated with other data for improving data interpretation in source rock studies. The method can use archived Rock-Eval analytical results, and no new samples are required for calculating kinetics. The resulting kinetic properties can be used in quick response to urgent needs in data interpretation for business decisions or for a first glance in numerical modeling of hydrocarbon generation history. The method can generate as many kinetic parameter pairs from all available pyrograms to form a population for a source rock system to examine the variation in transformation behaviors in space and time. The variation of the inferred kinetic parameters allows for examination of changes in kerogen composition within the same source rock unit in response to tempo-spatial variations in facies or climate and sea level, so that proper division of facies models can be applied in the modeling. The cost-effective and time-saving advantages of the new method come with a price. The trade-off for multiple heating rate laboratory experiments could be the potentially compromised accuracy, as suggested by Peters et al.31 However, our validation test suggests that the temperature discrepancy is about 1.5−2 °C in geological time scale for TR at 50 and 90/10 percentiles, respectively, for the Devonian Duvernay type II kerogen source rocks from WCSB, far less than the uncertainty range of formation temperature calculation and spatial extrapolation in the temperature field. This perceived weakness of the method is counterbalanced by its capability of generating a large number of kinetic estimates across a basin and computing numerous HI and Tmax pairs for comparing general trends of kerogen thermal decomposition for consistent analysis of a source rock system.
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(A4)
Wd 2 || F(m) − d ||2 Wm 2 || m − mapr ||2
(A9)
In the model stabilizer functional, the reference model mapr can play an important role during iterations. To obtain a global minimum of the parametric functional and a reasonable physical chemistry solution, we can make the reference
(A3)
Evidently, we can select {mαn } in such a way that for any n 1840
DOI: 10.1021/acs.energyfuels.6b01569 Energy Fuels 2017, 31, 1832−1841
Energy & Fuels
Article
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distribution mapr of activation energy be modeled as Gaussian distribution. mapr =
⎛ −(E − E )2 ⎞ 1 o ⎟ exp⎜ 2 σ 2π 2σE ⎝ ⎠
(A10)
To use the reweighted regularized conjugate gradient (RRCG) method for the minimization of the parametric function, it is necessary to calculate the first derivative of the data parameters with respect to the model parameters, i.e., the Fréchet derivatives, otherwise known as the Jacobians or sensitivities.
■
⎧ ∂P(m1) ∂P(mi) ∂P(mM ) ⎫ ⎬ ··· ··· Fm = ⎨ ∂mi ∂mM ⎭ ⎩ ∂m1
(A11)
AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This study is partly funded by the Program of Energy Research and Development (PERD) of Natural Resources Canada. This represents an output from the Geoscience for New Energy Supply Program. The authors thank Dr. D. M. Jarvie and two other anonymous journal reviewers for their constructive comments and suggestions. Our internal reviewer Dr. S. Grasby of the Geological Survey of Canada is thanked for his careful review and useful suggestions. The authors also thank Dr. D. Issler of the Geological Survey of Canada for helpful discussions on various methods of estimating hydrocarbon generation kinetics. ESS contribution # 20160165.
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REFERENCES
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DOI: 10.1021/acs.energyfuels.6b01569 Energy Fuels 2017, 31, 1832−1841
