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A Quick Evaluation of Source Rock Kerogen Kinetics Using Hydrocarbon Pyrograms from Regular Rock-Eval Analysis Zhuoheng Chen, XIAOJUN LIU, and Chunqing Jiang Energy Fuels, Just Accepted Manuscript • DOI: 10.1021/acs.energyfuels.6b01569 • Publication Date (Web): 16 Jan 2017 Downloaded from http://pubs.acs.org on January 17, 2017

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A Quick Evaluation of Source Rock Kerogen Kinetics Using Hydrocarbon Pyrograms from Regular Rock-Eval Analysis Zhuoheng Chen, Xiaojun Liu and Chunqing Jiang Geological Survey of Canada, Calgary [email protected]

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 modelling of hydrocarbon generation, kinetic parameters are often adopted from analogous source rock system available in published datasets, or are automatically picked by basin modeling software based on kerogen type or depositional environment and facies. Recent studies (Peters et al. 2006)1 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 business decision. Directly assessing reactivity and transformation behaviour of source rock based on archived Rock-Eval data would allow 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 (Jarvie, 2012a and b; Passey et al., 2010)2,3,4. 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 evaluation (Kuhn, et al., 2012)5 and identifying proliferous production zones (Hood, et al., 2012; Chen et al., 2016)6,7. The traditional approach for determining oil generation kinetics utilizes laboratory pyrolysis at variable heating rates to mimic the hydrocarbon generation processes (Aboulkas and Harfi, 2008)8,

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allowing 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 due to budgetary and time constraints. Results available in the public domain may also be problematic as they are not a direct reflection of a specific source rock or organofacies. For basin modelling 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 type (Kuhn, 2013)9 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), due to differences in their activation energy spectra (Peters et al. 2006; Chen et al, 2015)1,10. Furthermore, publically available source rock kinetic parameters are largely restricted to the well-studied basins, further limiting the possible analogues useful for data interpretation and petroleum system modeling. Another challenge for the conventional kerogen kinetics approach is that immature source rock samples, required for

laboratory pyrolysis analysis to derive the kinetics parameters, are not always available. An example of this is the Utica Shale in Quebec Canada, where the basin has undergone severe thermal alteration (Chen et al., 2014)11. Kerogen kinetics specific to a particular source rock unit is more desirable for characterizing the thermal transformational behavior of the source rocks. As 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 behaviour of target source rocks using archived RockEval data would allow people to position themselves with a competitive advantage, as Rock-Eval results are available for almost any source rock systems 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 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 utilized to demonstrate the application of the method in source rock evaluation.

2. Methods 2.1. Numerical model for kerogen conversion to hydrocarbons ACS Paragon Plus Environment

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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. (1990)12 and Dieckmann et al. (2004)13, including: 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 reactions and its contribution to the overall production rate depends on its abundance.

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 13 digitized from Dieckmann et al. (2004) , representing an immature source rock from 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 1a); c) aggregated hydrocarbon generation rate by kerogen component groups (in 1a) from


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the highest to the 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 horizontal axis. The outmost bell curve represents the total hydrocarbon generation potential; and d) cumulative product.

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 (e.g., Braun and Burnham, 1987; Issler, 1995; Waples and Nowaczewski, 2013)14,15,16. Li and Yue (2003)17 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 estimated frequency factors and activation energies for each sample. Issler (1995)15 studied methods using single, as well as variable, frequency factors, and found that the value of the estimated frequency factor depends largely on 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 Burnham (1987)14 and slightly different from the approach taken by Waples (2016)18 who used a fixed frequency factor for samples. Figure 1 demonstrates the assumptions and principles of our numerical model graphically. The histogram (Fig. 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 bell-shaped 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 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 reactions (Burnham and Braun, 1999)19:

= ∑ ( )

(1)

where j represents the jth component of x, aj is the relative abundance of jth component of x, kj is the reaction rate constant of jth component and m is the total number of kerogen compositional groups with ∑ = 1 and = ∑ . The absolute concentration is not important as all components are specified in terms of relative abundance.


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The temperature dependency of the reaction rate constant kj is quantified using the Arrhenius equation:

k = A ∙ exp −

(2)

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. By assuming a constant heating rate, defined by =dT/dt, the rate of conversion becomes a function of 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:

#

= ∑ () ! " = ∑ ∙ exp − ∙ ! "

(4)

While the conversion of the jth compositional group can be approximated by the following equation (Burnham, and Braun, 1999) 19: &

$' %( ) ( = $' k ()() ≈

#∙∙ + (1 ∙

−

, )exp(− )

(5)

The conversion of the bulk kerogen to hydrocarbon is then a convolution of the decomposition rates of kerogen components with the activation energy (Braun and Burnham, 1987)14: -

= ∑

#∙∙-+ ∙

∙ (1 −

,-+ )

∙ exp(− + ) ∙ ; -

i=1,2,..,n, and j=1,2,…,m

(6)

In Equation (6), we assume a nonparametric form of the density of activation energies, rather than a Gaussian distribution as suggested by Braun and Burnham (1987)14, and the shape of the distribution will be determined by data. In order to estimate the relative abundance of kerogen component, , an objective function, .(), is constructed by summing up all the differences in the estimated rates and relative abundances between the observed and the computed as follows:

, .() = ∑01( − ), + 3 ∑ ( − &45 ) , -

where and -

-/

-/

(7)

denote observed and computed rates, and and &45 are observed and computed

abundances. Parameter α is a weight for balancing the two terms in Equation (7). The problem in estimating the relative abundance of kerogen components in fixed groups in terms of activation energy and frequency factor in Equation (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


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referred to Zhdanov (2002)20. The numerical model and mathematical solution of this method is presented in Appendix A.

2.2. Rock-Eval analysis of source rock samples All Rock-Eval results on source rock samples were generated at the Geological Survey of Canada using Vinci Technologies’ Rock-Eval 6 instruments that can produce a TOC value. A finely powdered (< 212 µm) Cretaceous Second White Speckled shale sample with a 5.1% TOC and 441 oC Tmax has been used as a standard rock sample for the purpose of QA/AC of the Rock-Eval procedure. The standard sample was analyzed at both the beginning and end of every batch of samples, as well as between every 6 to 10 samples within the batch, to ensure the consistency of the Rock-Eval data generated over time. The amount of rock samples routinely loaded for Rock-Eval analysis is 70 mg; however, repeat analysis are undertaken at reduced amounts (e.g. 50 mg, 25 mg or 10 mg depending on organic richness) for any samples with high S2 and TOC values that may potentially saturate the instrument’s flame ionization detector (FID) for hydrocarbon detection and IR cell for CO2 and CO detection. As the combustion furnace of Rock-Eval 6 instrument was operated at 850 oC, at which the organic matter is assumed to be completely combusted, the TOC value obtained has been used as the “true” TOC content for the core samples and for the calculation of hydrogen index (HI) and oxygen index (OI) as well as kerogen transformation or hydrocarbon generation ratios in this study. A typical Rock-Eval hydrocarbon FID-pyrogram consists of three components: a) the S1 peak (mg HC/g Rock) for the amount of free hydrocarbons released during the 3 minute of isothermal heating at 300 °C from the rock sample; b) the S2 peak (mg HC/g Rock) that represents the amount of hydrocarbons that is generated from a source rock sample during the Rock-Eval pyrolysis stage from 300 to 650 °C at the heating rate of 25°C/minute, and that can be generated from a source rock upon further burial; c) Tmax, a measure of the temperature at the maximum of S2 peak, for the thermal maturity of the sample. Digital data of the S2 peaks are utilized in this study to derive the kinetics parameters using Equations (7).

3. Method Validation Utilizing the estimated kerogen kinetics reported for an immature source rock sample in Devonian Duvernay Formation from the WCSB by Dieckmann et al (2004)13, the rigorously measured and calculated kinetic parameters are taken as standard for the sample. This sample is labeled SAP and has the lowest thermal maturity among a series of samples with different maturities in their paper. The histogram in Figure 1a represents the distribution of activation energies of the kerogen with a frequency factor A=2.005e+16 1/min. Details of their laboratory procedure, source of the sample and other relevant information can be found in Dieckmann et al (2004)13.


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The relative contribution of each activation energy group to the overall production rate is computed at a heating rate of 25 °C/minute using Equation (5), and is shown as individual bell-shaped curves in Figure 1b. The aggregated production rates of all individual groups yield an overall production rate for the whole kerogen under a heating rate of 25 °C/minute. We used the same kinetic parameter set of SAP (Fig. 1a) to generate the overall production rates under different heating rates. We treat these production rate curves as they were generated from laboratory experiments of multiple heating rates to test our proposed method. Two general tests were performed: a) determining the distributions of apparent activation energies with a fixed frequency A at 2.005e16/min; and b) determining simultaneously both the apparent activation distribution and the frequency factor A via optimization using Eq. (7). Computer generated Rock-Eval curves from Equation (6) with five heating rates (1, 5, 10, 20, 25 °C/min) were plotted in Figure 2a to illustrate the variation of production rate with differing heating rates. When we fix A at 2.005e16/min, the method can reproduce all the pyrograms from the five heating rates very well, and the estimated activation energy distributions from the five heating rates are almost identical to the original distribution (Figure 2b).

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.

In the second test, we relaxed the restriction on A to allow for an optimization of A and activation energies simultaneously for each heating rate using the method described in Eq. (7). The estimated results, both activation energy and frequency factor A, are plotted in Figure 3 showing a systematic shift in both frequency factor A and the activation energy distribution. While the estimated factor A decreases with increasing heating rates (Figure 3b), the distribution of apparent activation energy shifts towards the lower side (Figure 3a), indicating a compensation effect of the two parameters. To investigate the potential impacts of the differences in estimated kinetic parameters on hydrocarbon generation history on a geological scale, the estimated apparent activation energy distribution and frequency factor A from the five different heating rates are used to calculate


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hydrocarbon transformation ratio (TR) in geological time, and the TR derived from the kinetic parameters of sample SAP is used as the “true” generation history for comparison. In the calculation, a geological heating rate of 2 °C/million years is used. The six TR curves look identical (Figure 4) at first glance, but careful examination finds that the five estimated hydrocarbon TR curves show small systematical shifts away from SAP towards the lower temperature side. Heating rate appears to play a key role in this shift. The higher the heating rate, the larger the shift from SAP is. However, the maximum shift among the five heating rates is less than 1.5 °C at 50% TR and less than 2 °C at 10 and 90% TR, respectively. Compared to the potential uncertainty associated with spatial extrapolation in temperature field (Chen et al., 2008)21, a 1.5-2.0 °C departure in transformation ratio calculation seems acceptable in hydrocarbon generation modeling in most cases.

Figure 3. a) Estimated apparent activation energy distribution with five different heating rates and comparison with the “True” distribution of SAP sample; b) Comparison of estimated frequency factor A from different heating rates with the “true” A from SAP.


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Figure 4. Comparison of kerogen transformation ratios (TR) constructed from the kinetics estimated using hydrocarbon pyrograms from Rock-Eval analyses at different heating rates with the TR calculated using the standard kinetics of SAP sample. A geological heating rate of 2°C/million years has been used for the TR calculation. The histogram inside the plot is the estimated activation energy distribution as compared against the distribution of SAP in Figure 1a.

4. Devonian Duvernay Shale Example, WCSB 4.1. Geological Setting The Duvernay Shale is a well-known petroleum source rock in the Devonian conventional petroleum system in south-central Alberta part of West Canada Sedimentary Basin (WCSB) (Creaney et al., 1994; Stasiuk and Fowler, 2002)22,23 (Figure 5) and is also a proven liquid-rich shale play. A horizontal well reported by Macedo (2013)24 had a 30-day average initial production rate of 1,400 bbls/day of light hydrocarbons and 4 mmcf/day of natural gas (Macedo, 2013)

24

, representing one of the best

unconventional resource wells in WCSB. The Duvernay shale was deposited under marine, deep-water, low-energy, basinal conditions surrounded by reefs and carbonate platforms with normal marine salinities in an oxygen-poor environment. These rocks are typically organic-rich, with present day TOC values of up to 15% and maximum hydrogen index close to 700 mg HC/g TOC (Chen and Jiang, 2016)7. It exhibits plane-parallel, millimetre-scale lamination (Creaney et al., 1994)22. Stasiuk and Fowler (2002 and


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2004)23,25 shows that maturity of the organic matter varies from immature in the north and east, to over-mature in the southwest close to the deformation front of the foreland basin in WCSB, with a large part of the Duvernay Shale lying in the wet-gas generation window. Recent studies indicate a strong positive correlation between the silica content and TOC content, which suggests a biogenic rather than detrital source for much of the silica (Dunn et al., 2012)26. Moreover, a strong positive correlation between increased reservoir quality (porosity and permeability) and TOC indicates an organic porosity dominated storage for the self-sourced and self-contained hydrocarbons (Dunn et al., 2012; Chen and Jiang, 2016)7,26. All Rock-Eval data used in this study are on core samples from organic rich Duvernay Shale from recently drilled pilot wells in the West Shale Basin (Figure 5). Six samples have been selected from five different wells that cover a wide range of thermal maturity from early mature to high maturity level (Table 1), and a large part of the basin from northwest to southeast gradually increasing in both depth and maturity (Figure 5). The key Rock-Eval analysis results are listed in Table 1. The sample C-598636 has the lowest thermal maturity indicated by Tmax =432 °C as well as the production index of 0.11 (Figure. 6a).

Figure 5. Map showing the areal extend of the Devonian Duvernay Shale and sample well locations in this study.

4.2. A link to an empirical model


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This part serves as a bridge connecting an existing empirical model (Chen and Jiang, 2015)10 with the proposed method here. The S2 curves of the pyrogram for all the six samples are superimposed in Figure 6a to show the progressive decrease of remaining hydrocarbon potential of kerogen with increasing maturity, as represented by the peak temperature (Tpeak), or the Tmax that is about 40 °C lower than Tpeak depending on the instrument condition. This clearly shows the gradual depletion of active kerogen components with increasing thermal maturation (Schenk and Horsfield, 1998) 27. The Tmax and HI values corresponding to the pyrograms are plotted on Figure 6b to depict the relationship between the kinetic behavior of the thermal decomposition of kerogen and Rock-Eval parameters. A statistical fitting of an empirical model to the observed HI and Tmax characterizes the thermal stability of various compositional groups of kerogen under thermal stress (Chen and Jiang, 2015)10. This empirical relationship is then converted to TR (Figure 6c) that represents the conversion of the source rock kerogen (Chen and Jiang, 2016)7. The two different expressions of kerogen thermal stability and transformation behaviors discussed above can be used jointly to support each other if necessary. When Rock-Eval data for a set of representative samples from a source rock system are available, the empirical model of hydrocarbon transformation ratio can be used to establish a reference model for validation of the pairs of Tmax and HI values computed from archived pyrograms. On the other hand, when the general trend of source rock thermal decomposition trajectory revealed by conventional Rock-Eval analysis is poor, computed HI and Tmax pairs from representative kerogen kinetics derived from one or more pyrograms may elucidate the general trend for data interpretation. Table 1. Rock-Eval analysis results for the Devonian Duvernay Formation showing general characteristics of the source rocks and remaining hydrocarbon potential at different thermal maturities in this study Depth (m) Well Lab ID TOC % S1 S2 S3 Tmax HI OI PI 4-34-77-23W5 C-598636 4.01 2.06 17.31 0.67 432 432 17 0.11 2409.18 7-22-69-21W5 C-598637 3.48 3.01 11.72 0.36 443 337 10 0.2 2701.65 8-15-62-18w5 C-579982 3.3 3.13 4.92 0.3 460 149 9 0.39 3016.73 8-15-62-18w5 C-579993 2.61 2.41 3.6 0.35 462 138 13 0.35 3028.56 15-33-41-8w5 C-598639 6.03 4.33 3.9 0.54 472 65 9 0.53 3452.65 1-24-61-23w5 C-598640 4.57 21 1.11 0.44 504 24 10 0.16 3709.58 Dieckmann 2004 E42790 8.58 420 604


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10000

a)

Tmax=432 Tmax=443

FID/iTOC

8000

Tmax=460 Tmax=462 Tmax=472 Tmax=504

6000 4000 2000 0 350

400

450

500

550

600

650

Temperature (°C)

HI (mg HC/g TOC

600

b)

Data Model

500 400 300 200 100 0 400

450

500

550

500

550

o

Tmax ( C) 1

c) Transformation ratio

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0.8 0.6 0.4 0.2 0 400

450 o

Tmax ( C) Figure 6. Hydrocarbon generation profiling based on Rock-Eval results for selected Duvernay source rock samples: a) superimposed pyrograms displaying the remaining hydrocarbon generation potential represented by S2 ; b) a cross plot of Tmax against HI displaying hydrocarbon conversion behaviour of the Duvernay source rock; and c) hydrocarbon transformation ratio converted from b).


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4.3. Comparison of the results from the proposed model with the empirical model Sample C-598636 is used to demonstrate the application of the proposed method for the study of source rock kinetics directly from archived normal Rock-Eval data. C-598636 has the lowest Tmax and highest HI among the six core samples (Table 1). A Tmax of 432 °C and a production index of 0.11 are indicative of an early mature stage in thermal decomposition. A numerical inversion by fitting the S2 curve from the pyrogram (Figure 7a) results in a set of kinetic parameters, represented by apparent activation energy and frequency factor A (Figure 7b). The remaining kerogen is characterized different ranges of activation energy (horizontal axis Figure 7b) at varying relative abundances (vertical axis of Figure 7b). The contribution of each kerogen group to the total remaining hydrocarbon generation is shown in Figure 7c, with each bell-shaped curve in Figure 7c corresponding to a bar in Figure 7b. The reaction rate of each kerogen component depends on its activation energy and the temperature, while its contribution to the overall hydrocarbon generation is determined by its abundance. Figure 7d is an aggregated remaining hydrocarbon generation potential starting from the kerogen group with the highest activation energy on the right toward the lowest on the left. Similar to Figures 6b and c, the peak temperatures of the bell-shaped curves (remaining potentials) are about a 40 °C upward shift from the Tmax values, and the total area under each bell-shaped curve yields a corresponding HI after scaled to unity TOC. Thus a number of Tmax and HI pairs can be calculated from Figure 7d and compared with real Rock-Eval data on samples of varying maturity levels.


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Figure 7. Duvernay Formation shale hydrocarbon generation profiling based on the normal single heating rate Rock-Eval result of an early mature source rock sample: a) comparison of the observed and the computer inversed S2 curves of the pyrogram for sample C-598636 from well 4-34-77-23W5; b) distribution of activation energy estimated by inversion method proposed in this study, with the five largest kerogen compositional groups color coded and marked from p1 to p6; c) thermal decomposition behaviours of individual kerogen components as represented by each activation energy interval; d) the calculated remaining hydrocarbon generation potential of the source rock at various maturities corresponding to differing peak pyrolysis temperatures.

Seven pairs of Tmax and HI values calculated from the estimated kinetics of sample C-598636 are plotted in Figure 8a. To construct the empirical model from the computed HI and Tmax results, a 15% evaporative loss in S1 peak has been assumed for estimating the initial hydrogen index (Jiang et al., 2016)28. With an estimated initial hydrogen index of 508, an empirical fitting model has been constructed using the calculated Tmax and HI values (Figure 8a). When the measured Rock-Eval data of the six samples in Table 1 are plotted in Figure 8a, they populate close to the fitting curve, indicating the robustness of the fitting model. The empirical model is then converted to a transformation ratio in Figure 8b. A comparison of the calculated Tmax and HI pairs from sample C-598636 and the real data pairs of the six core samples demonstrates that the computed data are a close approximation of the real ones (Figure 8b). This means that we can compute multiple HI and Tmax pairs from a single sample


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pyrogram, in cases that lack data points at higher maturity, to reveal the kerogen thermal decomposition pathway.

Figure 8. Hydrogen index data and model showing kerogen degradation trajectorial path with increasing thermal maturity indexed by Tmax and source rock thermal decomposition behaviours of the Devonian Duvernay Shale.

The reliability of the resulting kinetic parameters can be further validated with real Rock-Eval analytical results from a much larger set of the Devonian Duvernay Shale samples (Chen and Jiang, 2016; Jiang et al., 2016)7,35. The calculated data points are mixed with real data in Figure 9, and the constructed source rock thermal decomposition trajectory from the computed data pairs are comparable with the ones derived from analytical measurements.


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Figure 9. Comparison of the HI and Tmax pairs computed from sample C-598636 using the proposed method with the observed Rock-Eval results of a large set of Devonian Duvernay shale samples. The observed results are from 7

Chen and Jiang (2016) . Sample SAP from Dieckmann et al (2004)

13

is also plotted for comparison.

5. Discussion Rock-Eval analytical results contain information on kerogen thermal reactivity and hydrocarbon transformational behavior. For a typical Rock-Eval dataset, with a wide range of thermal maturity, each sample shows a specific thermal alteration status indexed by Tmax, while its remaining hydrocarbon generation potential is represented by hydrogen index (HI). When used jointly, these two parameters provide supplementary information with respect to hydrocarbon generation kinetics. To explore the potential use of routine Rock-Eval data for source rock kinetics, Chen and Jiang (2015)10 proposed an empirical model to quantify the relationship between these two parameters and then convert HI to hydrocarbon transformation ratio. In this paper, we discuss source rock kinetics by using regular Rock-Eval data rather than multiple temperature ramp laboratory experiments. The proposed method treats each pyrogram as an experiment and fits its S2 curve by a simplified, but meaningful mathematical expression of thermal degradation reactions of kerogen. This allows the kinetics of the remaining kerogen in the sample to be examined. The estimated apparent activation energy distribution and frequency factor A allow for characterization of the kinetic behaviors of different compositional kerogen groups, thus revealing the overall transformation behavior of the remaining kerogen and providing input parameters for petroleum system analysis or basin modeling. The method can also compute Tmax and HI values from the estimated kinetics to assist with data interpretation (Figure 9), or to be integrated with other data to provide a more representative kinetic model for oil and gas generation studies. There are two general applications for the proposed methods. Firstly, the estimated source rock kinetics from an immature source rock sample can be applied to basin modeling or petroleum system modeling. Because there could be a large number of immature samples, estimates of kerogen kinetics based on all available Rock-Eval data can be used to examine the impact of changes in kerogen composition in the same source rock system due to tempo-spatial variations in facies or climate and sea level. This allows that various organofacies models are examined and proper division of facies models can be applied in the modeling. Secondly, the method can be used to predict HI and Tmax of source rocks at various maturity levels, which can be used to compare to measured data. The computed Tmax and HI values can also be used to generate empirical transformation ratio models for hydrocarbon resource estimation (Chen et al, 2014 and 2016)

7,11

and other purposes such as organic porosity

estimation (Modica and Lapierre,2012; Chen and Jiang, 2016)

10,28,29

. The proposed method can be used

for estimating kinetic parameters in mature source rocks through the empirical transformation ratio modelling as shown in the study of Quebec Utica shale gas resource potential (Chen et al. 2014)11. More


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complicated kinetic inversion modeling allows direct estimation of kinetic parameters (frequency factor and distribution of activation energies) using a representing dataset of Tmax and HI measurements, which is out of the scope of this study. Figure 10 shows an example of using Rock-Eval pyrograms to help establish an empirical relationship between HI and Tmax for calculating hydrocarbon transformation ratios in a quantitative shale oil/gas 7

resource assessment of the Macasty Formation, Anticosti Basin in eastern Canada (Chen et al., 2016) . In this example, only one well reached 2500 m in depth across the basin, and the TR of the source rock remains unknown for deeper parts of the basin. Modeling hydrocarbon generation was hindered by large uncertainty in kerogen TR, particularly at higher maturity levels. The kinetics estimates of unconverted kerogen remnants from routine Rock-Eval pyrograms of samples at early maturity, or in the oil generation window, allow for estimating HI and Tmax pairs at higher maturity levels. This can reveal the kerogen TR profile and provide additional information for construction of the empirical model of hydrocarbon transformation.

Figure 10. Hydrocarbon generation model constructed from Rock-Eval data on the Macasty Formation of Anticosti Basin: a) kerogen decomposition is indicated by the trajectory path of decreasing hydrogen index with increasing Tmax; b) hydrocarbon transformation ratio (TR) is calculated from hydrogen index using an empirical relationship 30 between HI and TR in Chen et al(2016) .

The advantage of the proposed method is the direct use of archived regular Rock-Eval data and that no additional pyrolysis experiments are needed. This allows for a quick response to an urgent need for data analysis or for a first glance of kinetic parameters in basin modeling. The direct use of routine RockEval results permits estimation of kerogen kinetics from many samples to reveal a general trend of TR of a source rock unit or tempo-spatial variation of organofacies, thus building a representative model for petroleum system analysis and basin modeling.


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Representativeness and accuracy are two equally important issues in kerogen kinetics study, and can significantly affect data interpretation and numerical modeling of hydrocarbon generation. Utilizing only one experiment with a fixed heating rate, the proposed method may not be able to produce pairs of frequency factor A and activation energy distribution as accurate as the traditional multiple-heating-rate method can offer (Peters 2015)31. As shown in the above validation test, the estimated geological temperatures for hydrocarbon generation derived from the proposed method are comparable to those predicted using the traditional approach. For example, the temperature differences for 50% and 90% (and 10%) kerogen transformation between the proposed and the traditional methods are only 1.5 and 2.0 °C, respectively. Compared to the large uncertainty range in formation temperature determination (Chen et al., 2010 and Hu et al, 2014)32,33 and spatial extrapolation of temperature field (Chen et al., 2008)21, a deviation from the “true” temperature of 1.5 °C at TR 50% by this method is considered acceptable. As revealed in a study by Peters et al. (2015)31, potential variation of 50% TR temperature between single and multiple heating ramps for type III kerogen could show the largest variation. As our samples are from a type II kerogen source rock system, more tests are necessary for confirming the applicability of the proposed method to other kerogen types. However, transformational behavior of a source rock system constrained by large number of samples basin wide provide a better representative model for both modeling and data interpretation than that based on one or scattered samples. This is because variation of a source rock in terms of kerogen composition and organic richness is the intrinsic character of a natural system responding to changes in climate, supply of the source, depositional environmental facies and others (Fairbanks, et al., 2016)34. Our proposed method shows the capacity of providing a kinetic model and integrating additional data for constructing a consistent kinetic model with reasonably good accuracy.

6. Conclusions We proposed a method that uses pyrograms from regular Rock-Eval 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 utilize 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 kinetics 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 examination of


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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. (2015)31. However, our validation test suggests that the temperature discrepancy is about 1.5-2 °C in geological time scale for transformation ratio 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 temperature field. This perceived weakness of the method is counterbalanced by its capability of generating a large number of kinetics 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.

Acknowledgements This study is partly funded by PERD Program of Natural Resources Canada. This represents an output from 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 Geological Survey of Canada is thanked for his careful review and useful suggestions. We also would like to thank Dr. D. Issler of Geological Survey of Canada for helpful discussions on various methods of estimating hydrocarbon generation kinetics. ESS contribution #:

References (1) Peters, K.E.; Walters, C.C.; Mankiewicz P.J. AAPG Bulletin 2006, 90, 1–20, DOI:10.1306/08090504134. (2) Jarvie, D.M. AAPG Memoir 97, 2012, 69–87. (3) Jarvie, D.M. AAPG Memoir 97, 2012, 89–119. (4) Passey, Q.R.; Bohacs, K.M.; Esch, W.L.; Klimentidis, R.E.; Sinha, S. From oil-prone source rock to gasproducing shale reservoir – geologic and petrophysical characterization of unconventional shale-gas reservoirs: SPE 131350. 2010, (http://www.onepetro.org/mslib/servlet/onepetropreview?id=SPE-131350-MS). (5) Kuhn, P.P.; di Primio, R.; Hill, R.; Lawrence, J.R.; Horsfield, B. AAPG Bulletin 2012, 96, 1867–1897. DOI:10.1306/03261211063. (6) Hood, K.; Yurewicz, D.A.; Steffen, K.J. Bulletin of Canadian Petroleum Geology 2012, 60, 112-133.


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(7) Chen, Z.; Jiang, C. AAPG Bulletin. 2016, 100, 405-422, DOI:10.1306/08261514173. (8) Aboulkas, A.; Harfi, K. EL. Oil Shale 2008, 28, 426-443. (9) Kuhn,P.P.; Keym, M.; Podlaha, O.; di Primio, R. Search and Discovery Article #120129. Posted March 13, 2013, http://www.searchanddiscovery.com/documents/2013/120129kuhn/ndx_kuhn.pdf (10) Chen Z.; Jiang C. Marine and Petroleum Geology 2015, 67, 795-803. (11) Chen, Z.; Lavoie, D.; Malo, M. Geological Characteristics and Petroleum Resource Assessment of Utica Shale, Quebec, Canada; Geological Survey of Canada, Open File 7606, 2014, DOI:10.4095/293793 (12) Schaefer, R.G.; Schenk, H.J.; Hardelauf, H.; Harms, R. Advances in Organic Geochemistry 1990, 115– 120. (13) Dieckmann, V.; Fowler, M.; Horsfield, B. Organic Geochemistry 2004, 35, 845-862. (14) Braun, R. L.; Burnham, A. K. Energy and Fuels 1987, 1, 153-161. (15) Issler D.R. Geological Survey of Canada Open File 3001.1995, 73 pages, doi:10.4095/195126. http://geoscan.nrcan.gc.ca/starweb/geoscan/servlet.starweb?path=geoscan/fulle.web&search1=R=195 126 (16) Waples, D. W.; Nowaczewski, V. S. 2013, Source-rock kinetics, accessed February 6, 2015, https://siriusdummy.files.wordpress.com/2013/11/perspective-on-sr-kinetics-ss.pdf. (17) Li, S. and Yue, C., Fuel. 2003, 82, 337–342 (18) Walpes, D. W., AAPG Bulletin, 2016, 100(4), 683-689. (19) Burnham, A. K.; Braun, R. L. Energy and Fuels 1999, 13, 1-22. (20) Zhdanov, M.S. Geophysical inverse theory and regularization problems. Elsevier Science, p.633, 2002. (21) Chen, Z.; Osadetz, K.G.; Issler, D.R.; Grasby, S.E. AAPG Bulletin. 2008, 92, 1639-1653. (22) Creaney, S.; Allan, J.; Cole, K. S.; Fowler, M. G.; Brooks, P.W.; Osadetz, K. G.; Snowdon, L. R.; Riediger, C. L. Petroleum generation and migration in the Western Canada Sedimentary Basin; in Geological Atlas of the Western Canada Sedimentary Basin, G.D. Mossop and I. Shetsen (comp.), Canadian Society of Petroleum Geologists and Alberta Research Council, 1994. (23) Stasiuk, L.D.; Fowler, M.G. Thermal maturity evaluation (vitrinite and vitrinite reflectance equivalent) of Middle Devonian, Upper Devonian, and Mississippian strata in the Western Canada Sedimentary Basin: Geological Survey of Canada, Open File 4341. 2002. (24) Macedo, R. Duvernay Well Encouraging for Encana: Daily Oil Bulletin, April 24, 2013. (25) Stasiuk, L.D.; Fowler, M.G. Bulletin of Canadian Petroleum Geology 2004, 52, 234-256. (26) Dunn, L.; Schmidt, G.; Hammermaster, K.; Brown, M.; Bernard, R.; Wen, E.; Befus, R.; Gardiner, S. The Duvernay Formation (Devonian): Sedimentology and reservoir characterization of a shale gas/liquids play in Alberta, Canada: GeoConvention 2012: Vision, Calgary, Alberta, Canada.


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(27) Schenk, H. J.; Horsfield, B. Germany. Org. Geochemical 1998, 29, 137-154. (28) Jiang, C.; Chen, Z.; Mort, A.; Milovic, M.; Robinson, R.; Stewart, R.; Lavoie, D. Marine and Petroleum Geology. 2016, 70, 294-303. (29) Modica, C. J.; Lapierre, S. G. AAPG Bulletin 2012, 96, 87–108. (30) Chen, Z.; Lavoie, D.; Jiang, C.; Duchesne, M.J.; Malo, M. Geological Characteristics and Petroleum Resource Assessment of the Macasty Formation, Anticosti Island, Quebec, Canada, Geological Survey of Canada, Open File 8018, 2016, DOI: 10.4095/297865. (31) Peters, K. E.; Burnham,A. K.; Walters, C.C. AAPG Bulletin 2015, 99, 591–616. (32) Chen, Z.; Grasby, S. E.; Dewing, K. Temperature-depth plots for selected petroleum exploration wells, Canadian Arctic Islands Geological Survey of Canada, Open File 6567, 2010. DOI:10.4095/262738 (33) Hu, K.; Chen, Z.; Issler, D.R. Determination of geothermal gradient from borehole temperature and permafrost base for exploration wells in the Beaufort-Mackenzie Basin; Geological Survey of Canada, Open File 6957, 2014, DOI:10.4095/293872. (34) Fairbanks, M. D.; Ruppel, S. C.; Rowe, H. AAPG Bulletin. 2016, 100, 379–403. (35) Jiang, C., Obermajer, M., Su, A., Chen, Z. Rock-Eval/TOC Analysis of Selected Core Samples of the Devonian Duvernay Formation from the Western Canada Sedimentary Basin, Alberta. Geological Survey of Canada Open File 8155. 2016, 532p.

Appendix A: Minimization of parametric function Let us assume that 6(7) is a continuous operator from a model space 8 to a data space 9. For any ( ∈ 9 and any parameter 3 ≥ 0, there is a model 7= ∈ 8, on which the functional .= (7), equation (7), reaches its lower boundary: >?@ ∈A .= (7) = .= (7= ).

(A1)

There is the exact lower boundary of the smoothing functional BC .= (7) = .= (7D ),

(A2)

because for any 7, .= (7) ≥ 0. Thus, we can select a sequence from the models E70= F, such that lim0→K .0= (7) = .D= .

(A3)

Evidently, we can select E70= F in such a way that for any C = .0L ≤ .0= ≤ .=

Then for any C and for any fixed 3 ≥ 0


(A4)

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3N(70= ) ≤ .0= ≤ .=

(A5)

Suppose that 3 > 0

N(70= ) ≤ = .= ≤ c.

(A6)

Thus, the sequence of the models E70= F belongs to a subset 8Q ∈ 8, for which N(7) ≤ c. According to the definition of the stabilizing functional, the subset 8Q is a compactum. Therefore, we can select from = the sequence E70= F, a sub-sequence R70(S) T, which converges to some 7= ∈ 8. Inasmuch as operator

6 is a continuous operator

,

= = BC ∈A .= (7) = lim0→K .0= (70= ) = limS→K .0= !70(S) " = limS→K UV6!70(S) " − (V + = 3N!70(S) "W = ‖6(7= ) − (‖, + 3N(7= )

(A7)

In the case when 3 = 0, the parametric functional is equal to the stabilizing functional for which there exists a model minimizing its value. From this statement, Theorem (A1) follows. Since the minimization of parametric functional .= (7= ) is solvable, we use a gradient-type technique, the regularized conjugate gradient (RCG) method (Zhdanov 2002)20 to calculate the unknown parameters, as shown in the following steps: Z0 = 6(7) − (

(A8)

[0=0 = [ =0 (70 ) = @0∗ ], Z0 + 3] , (7 − 7&45 ) =0` ^0=0 = ‖[0=0 ‖, /V[0` V

,

=0` [a0=0 = [0=0 + ^0=0 [a0`

[a'=' = ['=' , , 0=0 = ([a0=0 [0=0 )/EV] @0∗ [a0=0 V + 3V] [a0=0 V F

70L = 70 − 0=0 ∙ [a0=0 where: 6(7) is the general analytical solution of pyrolysis and we assume a first-order reaction: () = 1 − as commonly applied (i.e., Burnham 1999)19; Z0 is the residual in data space; [0=0 is the gradient direction; @0∗ is the adjoin operator of Frechet derivative matrix; 7&45 is the reference model; 0=0 is the step length, ( is the measured reaction rate or cumulative reaction peak value of each sample; 7 is the unknown modeling parameter. ] is the data weighting, ] is the model weighting. The appropriate selection of ] and ] is very important for the success of the inversion. 3 is regularization parameter which represents the subsequent values of the regularization parameter at the Cb iteration and can provide a balance between the misfit and stabilizing functional. The first value of the regularization parameter is determined after first iteration:


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3D =

cd+ ‖e( )`‖+

+

+ V ` cf ghi V

(A9)

In the model stabilizer functional, the reference model 7&45 can play important role during iterations. In order to obtain a global minimum of parametric functional and a reasonable physical chemistry solution, we can make the reference distribution 7&45 of activation energy to be modeled as Gaussian distribution: 7&45 = j

`(` )+ exp ( ,j+/ ) ,l √ m

(A10)

In order to use the Reweighted Regularized Conjugate Gradient method (RRCG) 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: @ = E

no( p ) no( ) no( ) ⋯ n - ⋯ n r F n p r


(A11)

Quick Evaluation of Source Rock Kerogen Kinetics ... - ACS Publications

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