Article pubs.acs.org/EF
A Simple Kinetic Model of Oil Generation, Vaporization, Coking, and Cracking Alan K. Burnham* Department of Energy Resources Engineering, Stanford University, Stanford, California 94305-2220, United States ABSTRACT: A simple model is presented that accounts for the effects of temperature, pressure, and externally supplied gas flow rate on the kinetics of oil evolution during oil shale pyrolysis. The primary transport mechanism for generated oil from retorting oil shale particles is, by far, vaporization in co-generated gases. The simple model is based on the concept that an equivalent volatility of the oil must be achieved in order to attain the same extent of oil evolution from the particle. Oil generated at lower temperature (hence, lower volatility) must undergo additional coking and cracking reactions to reach equivalent volatility, and that effect can be modeled by adding a simple term to the effective activation energy. This simple approach explains much of the compensation effect observed in the literature between apparent activation energies and frequency factors derived under different pyrolysis conditions. A similar approach can model the effect of pressure on oil evolution. The effect of pyrolysis temperature on volatility is reduced in the presence of an external purge gas, and the effect of the additional temperature term can be reduced by dividing it by a dimensionless flow rate. Simple correlations are presented between oil yield and various product quantities and qualities, as well as inter-relationships among various product properties for the Green River oil shale. Although these effects have been modeled more rigorously by coupling chemical kinetic models to vapor−liquid equilibrium models, the current model is simpler to incorporate into integrated process models. Generalization to other rocks is discussed briefly.
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where k is the rate “constant”, A the frequency factor, E the activation energy, R the gas constant, and T the absolute temperature. This rate constant can be combined with a rate law to describe the reaction rate:
INTRODUCTION It has been known for many years that shale oil quality evolves through a series of coking and cracking reactions that are coupled to mass-transfer processes,1 and detailed models involving coupled vapor−liquid equilibria and secondary reactions have been developed.2,3 However, integrated process models can benefit from simple algorithms that predict how heating rate and pressure affect vaporization, oil and gas yields, and oil properties, because the numerical burden of dealing with these kinetic processes in a rigorous manner can be problematic. In this paper, data from a wide range of experiments at multiple laboratories are used to derive a simple kinetic model of oil generation, vaporization, coking ,and cracking. The overall effect, which has been known for many years but not recognized by many, is that the generation of oil at a lower temperature over longer times delays oil vaporization and escape from the reactor, thereby allowing reactions that coke aromatic heterocycles and crack long alkyl chains, which leads to a lighter product with fewer heteroatoms and trace metals.1 Depending on market conditions, this crude shale oil can become more valuable, because it is more readily transported and introduced into refineries. However, this potential increase in unit value must be counterbalanced by the decrease in oil yield and increase in less-valuable gas. Being able to model the secondary reactions in any given process can help optimize the economics of that process by adjusting the retorting parameters to improve the value of the produced products.
dα = k(T (t ))f (α) dt
where α is the fraction reacted, t is the time, and f(α) is a form function. The separation of the rate constant from the form function is itself an approximation, because it is incorrect for competing reactions. However, eq 2 usually works well, especially when complex materials are broken into a set of independent parallel reactions, each described by eq 2. Sequential and branched reactions can be described by systems of equations of the form of eq 2, as long as specific molecules or lumped species can be adequately defined and quantified. Sometimes, the progression along the reaction coordinate is described by an array of A−E pairs versus conversion. This approach is called isoconversional kinetics and is mathematically equivalent to a system of infinitely sequential first-order reactions.4 There are hundreds of determinations of kerogen pyrolysis kinetics in the literature. Unfortunately, many report parameters that are not generally reliable in the sense of being able to predict data not used in their calibration. Novices to kerogen pyrolysis kinetics are commonly unable to discern reliable from unreliable approaches and often propagate poor methodologies. Poor methodology is the primary cause for the commonly observed compensation relationship between
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CHEMICAL KINETICS BACKGROUND The usual starting point for chemical kinetics is the Arrhenius relationship: k = Ae−E / RT
Received: September 7, 2015 Revised: October 15, 2015 Published: October 29, 2015
(1) © 2015 American Chemical Society
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Energy & Fuels Table 1. Kinetic Studies of Oil Generation from Green River Oil Shale Used in This Analysis reference
type of reactor
temperature range (°C)
temperature schedule
Shih and Sohn12 N. D. Stout13 Campbell et al.14 Campbell et al.15 Burnham and Singleton16 Wallman et al.17 Braun and Burnham18 Freund and Keleman19 Braun et al.20 Burnham et al.21 Tegelaar and Noble22 Burnham23 Ruble and Lewan24 Hillier et al.25 Peters et al.26 Wellington et al.27 Bunger and Plikas28 Burnham and McConaghy29
fluidized bed cylindrical reactor cylindrical reactor and TGA cylindrical reactor semiopen cylindrical reactor fluidized bed fluidized bed quartz reactor with purge Pyromat II fluidized bed and Pyromat Pyromat II cylindrical reactor hydrous pyrolysis and Rock-Eval TGA Pyromat II and SR Analyzer semiopen autoclave cylindrical reactor semiopen autoclave
360−500 300−500 300−475 300−600 300−500 425−540 480−540 210−390 300−550 350−510 300−550 300−480 250−500 300−500 300−500 200−400 230−390 300−430
ramp interrupted ramp ramp and isothermal ramp ramp isothermal isothermal isothermal ramp ramp and isothermal ramp ramp isothermal and ramp ramp ramp ramp ramp ramp
activation energy and frequency factor in the literature. The compensation relationship arises because a range of correlated A and E values can match measured rate constants to within experimental accuracy over a narrow range of temperature. Poor methodology can be summarized into five categories: (1) Some studies assume first-order kinetics for what is really a broad range of consecutive and sequential reactions. If the degree of conversion is not adequately decoupled from the pyrolysis temperature, the same set of reactions is not represented at each temperature, and, depending on the structure of the kerogen (linear or branched), the apparent activation energy can be higher or lower than the true value. This is a common problem when using isothermal experiments. (2) Some studies perform a single experiment at a constant heating rate and fit that reaction profile to a first-order reaction. This practice was common in the past, but methodology developed and published independently at the Institut Français du Pét role (IFP)5 and Lawrence Livermore National Laboratory (LLNL),6 as well as two papers by the ICTAC Kinetics Committee,7,8 have drastically reduced the use of this erroneous approach. As with category (1), the derived activation energy can be higher or lower than the true value. Software is available for purchase (e.g., Kinetics2015 and AKTS-Thermokinetics) that can properly fit a wide range of global kinetic models. (3) Some studies using multiple heating rates do not use a range of heating rate that is wide enough and replicate measurements to adequately constrain A and E. There are an infinite number of A−E pairs that can predict the reaction rate at a given temperature. The challenge is to have enough accurate data over a sufficiently wide temperature range to adequately locate the centroid of the ellipsoidal minimization surface. Even the best analysis software cannot overcome the limitations of bad data. (4) Temperature errors can be a function of pyrolysis temperature and heating rate, because of both transient and steady-state variations in temperature profiles within the reactor. These nonrandom errors lead to inaccurate measurement of the apparent reaction rate versus temperature, which is converted to an erroneous A−E pair.
(5) Kerogen pyrolysis experiments at different temperatures and pressures generate different volatile products, because of varying degrees of secondary reactions caused by differences in volatility of the primary products at the generation conditions. The use of a purge gas can further modify the residence time of the primary products in the reactor. Consequently, the apparent activation energy and frequency factor contain contributions that are due to vaporization limitations and secondary reactions that are not commonly recognized or understood. Previous papers have explored the effects of incorrect model assumption,9,10 systematic temperature measurement errors,6 and random measurement errors11 on the kinetic parameters. Finding a simple way to relate true and apparent kinetic parameters from category (5) effects is the objective of this paper. This paper will show that these effects can be treated with an extremely simple equation: Eeff = Etrue +
5(1 − T /500°C)2 + 67(Pa − 1) (1 + F )
(3)
where Eeff is the instantaneous effective activation energy (in kcal/mol), Etrue the true activation energy in the absence of vaporization limitations, T the temperature (in Celsius), F a dimensionless external flow rate, and Pa the absolute pressure (in bar). The paper systematically addresses the methods to calibrate the coefficients associated with T, Pa, and F.
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BRIEF OVERVIEW OF GREEN RIVER OIL SHALE KINETICS There is a huge amount of literature on Green River oil shale kinetics, because of its historical potential as a source of synthetic crude oil and its generation of conventional crude oil in the Uinta Basin. The current analysis considers only a representative sample of available measurements, with the specific objective of developing a single rate expression that can describe the formation of volatile oil over a very wide temperature range and a time scale variation of 5 orders of magnitude. This range of conditions spans the rapid generation of a heavy synthetic crude oil in a fluidized bed to the in situ generation of a light synthetic crude over a time scale of months. The selected studies are listed in Table 1.12−29 7157
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parameters derived33 from the hydrous data of Huizinga et al.32 for Green River shale. The high A−E values from hydrous pyrolysis have been proposed to be caused by mass transport limitations,33 but a full discussion of hydrous pyrolysis is outside the scope of this article. Burnham measured the kinetics of evolution of oil from a self-purging reactor for a variety of source rocks heated at 2 °C/ min and 2 °C/h. The term “evolution” in this context means to evolve or be expelled from the reactor, which occurs almost exclusively by vaporization. The derived activation energies were systematically ∼5 kcal/mol higher than measured using the Pyromat II apparatus, which uses small samples swept with helium during pyrolysis. Even so, the evolution curves calculated from the Pyromat II kinetic parameters agreed well with the oil evolution experiments, suggesting that the compensation effect was operative. The increase in apparent activation energy and frequency factor was attributed to vaporization limitations at the lower heating rate. The increasing importance of product volatility on apparent kinetic parameters becomes even more important from reanalyzing data reported recently by Bunger and Plikas28 for pyrolysis of Green River oil shale when gradually heated over 7, 90, and 210 days, respectively. The fits and kinetic parameters derived from that data are shown in Figure 3. The primary apparent activation energy of 62 kcal/mol of the parallel reaction model is between that of Lewan and Ruble24 and Burnham.23
Figure 1 plots the frequency factor and activation energy parameters from these various studies. When a parallel reaction
Figure 1. Compensation effect plot for various determinations of the Arrhenius parameters for pyrolysis of Green River oil shale and kerogen. The filled circle was derived from the data of Bunger and Plikas,28 and the blue solid line is calculated from a simple vaporization-limited oil evolution model defined in a later section, starting at the circle for the most probably true A and E and ending at the square for the lowest heating rate pair. The outliers with high and low activation energies are from refs 24 and 27, respectively.
model was used, the primary A and E values are plotted, which is valid given that Green River shale kinetics are dominated by a single E value. A compensation effect is evident, in which A and E vary in a correlated manner for reasons discussed in detail by Stainforth.30 The center of the cluster is close to 3 × 1013 s−1 and 52.5 kcal/mol. The outliers are those from Wellington et al.27 at the low end and Lewan and Ruble24 at the high end. Wellington’s parameters are far outside the range of other measurements, including those by Klomp and Wright31 from the same company. Stainforth clearly supports kinetic parameters near the center of Figure 1 and specifically rejected the outlying hydrous pyrolysis kinetics of Lewan and Ruble.24 By itself, Figure 1 does not give a good estimation of the difference in predicted rate constants. The two extreme pairs and a probable set near the middle of the central cloud of determinations are compared in Figure 2. Wellington’s
Figure 3. Fit of pyrolysis data for Green River oil shale from Bunger and Plikas28 to a parallel reaction model. Black points represent data for a 210-day experiment, red points represent data for a 90-day experiment, and blue points represent data for a 7-day experiment.
Disregarding the kinetic parameters of Wellington et al., the lower E range (44−52 kcal/mol) are often from fluidized-bed pyrolysis near 500 °C, and the higher activation energies are derived from unpurged pyrolysis experiments at lower temperatures. The activation energy of 50 kcal/mol derived by Freund and Kelemen19 is particularly interesting, in that they used very low temperatures but recirculated gas through the pyrolysis region and monitored the buildup of octane and butane. This activation energy is close to the values derived from fluidized beds, suggesting that their purge system eliminated the volatility limitations of typical kinetic experiments conducted at low temperature. The reason for the change in activation energy, as a function of pyrolysis temperature and purge, becomes clear if one considers the changes in oil properties to be a function of the pyrolysis conditions. Ryan et al.34 plotted density data from Shell and LLNL and showed that API gravity correlated well with the logarithm of heating rate over 5 orders of magnitude
Figure 2. Comparison of the outlying kinetic expressions with an expression from the center of most determinations.
parameters appear to give plausible predictions only at the very low temperatures (∼260 °C) of Shell’s in situ oil shale retorting process. Their predictions are off by a factor of 10− 100 for normal laboratory conditions. The kinetic parameters of Lewan and Ruble24 are substantially slower below 350 °C than those determined from typical pyrolysis, and they are similar to 7158
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Energy & Fuels from Fischer assay (∼12 °C/min) to 0.5 °C/day. The API gravity change was caused by a systematic decrease in boiling point distribution and increase in hydrogen content. This trend is consistent with earlier observations of a decrease in nitrogen content due to coking reactions,13,15 which are enhanced at lower heating rates by longer liquid-phase residence times due to lower vapor pressure. In fact, one can interpret the higher apparent activation energy observed as heating rate declines by an increasing delay between oil generation and vaporization, during, which coking and cracking reactions, work along with the increasing temperature to achieve an equivalent volatility. A similar effect is observed when pyrolysis in a self-purging reactor occurs at elevated pressure. Higher temperature is required to achieve equivalent vapor volatility, thereby shifting the evolution profile to higher temperature.16,29,35 The shift can be modeled rigorously by coupling vapor-equilibrium calculations to chemical kinetics,2,3 but it can be modeled more simply by making either the frequency factor27 or the activation energy29 a function of pyrolysis pressure.
considered to be for the generation of 22.5 API gravity oil typical of rapid pyrolysis. Choosing the Temperature Adjustment Function. The next step is to choose and calibrate a way to account for the effect of delayed vaporization at atmospheric pressure in a simple, empirical manner. It so happens that the kinetics of unpurged oil evolution can be modeled simply by making the activation energy of oil evolution (as distinct from oil generation) a function of temperature, to mimic the effects of oil vapor pressure and secondary cracking on the oil evolution temperature. The temperature factor must have the property that it is approximately zero at 500 °C and increases as temperature decreases. An exponential function might be appropriate due to the exponential dependence of vapor pressure on temperature; however, after testing a few options, a simpler function was chosen that works as well and is computationally faster for use in integrated process models. The resulting effective energy function is
CALIBRATING THE EQUIVALENT VOLATILITY KINETIC MODEL Choosing the True Activation Energy. The first step in calibrating eq 3 is to choose values for A and Etrue. The predominance of activation energies in Figure 1 are in the 50− 56 kcal/mol range, but given the evidence that vaporization can affect the apparent value, it is likely that the value of Etrue is in the 50−53 kcal/mol range. I chose Etrue = 52 kcal/mol, which is slightly lower than that derived by Shih and Sohn using isoconversional kinetic analysis of fluidized-bed pyrolysis data for 0.3−2.4 mm particles.12 One could as easily argue for the value of 51 kcal/mol chosen years ago in a similar exercise,6 but it simply is not known to any better than ±1 kcal/mol. The corresponding A value for 52 kcal/mol is 2 × 1013 s−1. From Figure 1, a shift of 1 kcal/mol is compensated by a factor of 2 in A, so A is constrained to be between 1 × 1013 s−1 and 4 × 1013 s−1. To get some idea of the possible error in the chosen A and E values, the extents of reaction at 470 and 511 °C are compared in Figure 4 to that predicted from parameters of Shih and Sohn12 and Burnham et al.21 The latter were calibrated using a fluidized bed operating at those temperatures. The calculated rates from the chosen parameters fall between these two literature measurements and might be considered to be accurate to approximately ±20%. These parameters can be
(4)
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2 ⎛ T ⎞ ⎟ Eeff = Etrue + 5⎜1 − ⎝ 500 °C ⎠
where T is expressed in Celsius, the energies are given in kcal/ mol, and the factor of 5 was determined by comparison to various experiments from the literature, particularly the works of Burnham23 and Bunger and Plikas,28 as described below. At T = 300 °C, which is an appropriate temperature for in situ retorting, the effective activation energy increases by only 0.8 kcal/mol, which seems insignificant, but it actually causes the rate of oil evolution to be only 40% that of oil generation. At a heating rate of 1 °C/day, that inhibition causes the midpoint of oil evolution to be shifted upward by ∼20 °C. To determine the effect on evolution temperatures and kinetic parameters as they are ordinarily determined, synthetic evolution curves were generated for the true generation kinetic parameters of A = 2 × 1013 s−1 and Etrue = 52 kcal/mol, with (evolution) and without (generation) the temperature adjustment factor, at six heating rates ranging from 60 °C/min to 1 °C/day. Generation and evolution results for three heating rates are shown in Figure 5. One can see the increasing delay
Figure 5. Comparison of calculated generation of 22.5° API gravity oil (dashed line) with evolution of lighter oil after coking and cracking from an unpurged reactor (solid line).
for oil evolution compared to oil generation as heating rate decreases. Pairs of synthetic evolution curves were then analyzed using Kissinger’s method36 to determine the apparent activation energies (Eapp) and frequency factors at different heating rates (see Table 2).
Figure 4. Comparison of hydrocarbon generation rate calculated from the chosen values of A and Etrue (2 × 1013 s−1 and 52 kcal/mol, respectively) with two rate expressions derived from fluidized-bed experiments.12,21 7159
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Energy & Fuels Table 2. Apparent Rate Parameters from Synthetic Data Calculated Using a Temperature-Dependent Activation Energy As Described in eq 3 low heating rate
high heating rate
Aapp (s−1)
Eapp (kcal/mol)
6 °C/min 3.6 °C/h 0.86 °C/day
60 °C/min 36 °C/h 8.6 °C/day
1.2 × 10 1.8 × 1015 1.7 × 1016
54.6 58.4 61.2
14
One might be surprised that the apparent activation energies are so much higher than the temperature-dependent effective activation energy. However, the effect of the energy correction at any given temperature is magnified when one compares its effect at two different temperatures, which is the nature of an experimental determination. In fact, R × d(lnk)/d(1/T) is not simply E but rather E + 5[1 − (T2/5002)]. The Eapp values in Table 2 are slightly different from this relation because they are derived over intervals rather than a fixed temperature. The frequency factor changes in accordance with the compensation effect to calculate the correct reaction rate over the temperature range of calibration. Also noteworthy is that the variation in kinetic parameters is consistent by design with the observed experimental trends. Campbell’s14 and Pyromat21,22 kinetics for Green River oil shale are typically in the mid- to low-50 kcal/mol range, which is consistent with the first line in Table 2. Burnham’s oil evolution kinetics23 extending down to 2 °C/h are consistent with the second line, and oil evolution kinetics derived from Bunger’s data28 are consistent with the third line. The parameters in Table 2 are plotted along with the true A and E values in Figure 1, and one can see that the resulting curve follows the large body of reported results. In addition, the calculated true Tmax of 484 °C at 25 °C/min is within the range of reported measurements, keeping in mind that one must subtract ∼38 °C to compare to the commonly reported RockEval Tmax value.6 The first 5% or so of the oil volatilized from Green River oil shale is rich in biomarkers and represents a combination of the evaporation of C13−C35 components in the native bitumen and the breakdown of labile kerogen, which also yields a pyrolysate that is rich in biomarkers.37 This requires a parallel reaction model for best results. The early oil can be modeled by either using a larger A value, using a lower E value, or changing both along some compensation line.2,3 For numerical simplicity, the model proposed here merely multiplies the frequency factor for the first 5% of the oil by 50, which shifts the early oil evolution temperature by ∼50 °C. The calculated fractions of evolved oil using this model agree well with the data from the works of Bunger28 and Burnham,23 as shown in Figure 6. The heating rate was not constant in Bunger’s data, and the calculation used the average heating rate over the oil generation interval. In addition, the 50% evolution temperatures of 365 and 373 °C, respectively, at a rate of 2 °C/h from the works of Burnham and McConaghy29 and Campbell et al.15 agree well with the results presented in Figure 6. Validating the Pressure Adjustment Function. Burnham and Singleton16 showed how a back-pressure regulator delayed the evolution of oil from a self-purging reactor at different heating rates, and Burnham and McConaghy29 showed how the magnitude of the delay was dependent on the amount of back pressure. The latter paper proposed that the effect could be modeled simply by adding a pressuredependent term to the effective activation energy. To be clear,
Figure 6. Comparison of eq 4 (lines) with the data (points) from the works of Bunger and Plikas28 (top) and Burnham23 (bottom).
this is not a change in the intrinsic activation energy for the pyrolysis reactions, although there could be a minor contribution from an activation volume. It is an empirical factor to accommodate the need for some combination of increased temperature and coking and cracking reactions to enable the oil to reach equivalent volatility. Neglecting the effect of an external purge gas, which is not relevant for these two papers, the effective activation energy becomes 2 ⎛ T ⎞ ⎟ + 67(P − 1) Eeff = Etrue + 5⎜1 − a ⎝ 500 °C ⎠
(5)
Equation 5 is tested against the data of Burnham and Singleton in Figure 7. This comparison is not a fitthe
Figure 7. Comparison of eq 5 with the data of Burnham and Singleton.16
parameters in eq 5 were derived from other experiments. The agreement is good, and the deviations between measurement and calculation are not systematic and may represent experimental error. This favorable comparison both validates the temperature correction function and suggests that this simple pressure adjustment function is generally applicable. 7160
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Energy & Fuels Effect of Temperature and Pressure on Oil Yield. As noted earlier, part of the effects being modeled by modeled by eqs 4 and 5 are the increase in oil volatility due to coking and cracking reactions. These reactions, of course, come with an oil yield penalty and other changes in oil properties. The former is presented now because of its utility for calibrating the effect of a purge gas, and the latter are presented in a later section. The effect of heating rate on oil yield has been documented thoroughly in various papers from LLNL.1,15,16 Those results are plotted in Figure 8, along with more recent published
Figure 9. Relationship between nonisothermal oil yield and oil generation temperature, compared to isothermal experiments.38,39
between the generation and evolution temperatures, with an asymptotic limit of 20% yield loss, as determined in Figure 8. Choosing the Purge Gas Adjustment Function. As noted earlier, the oil yield loss at atmospheric pressure in a full reactor is due primarily to liquid-phase coking and cracking, which, in turn, relates to the delay between generation and vaporization of the oil species. Oil yields from small particles (i.e., those for which the characteristic time for gas diffusion is less than the characteristic time for pyrolysis) can be increased by adding a purge gas that aids in the vaporization of the generated oil. Figure 10 shows the effect of purge-gas flow rate
Figure 8. Relationship between oil yield and heating rate compiled from various literature sources. Yields from high-pressure retorts do not fall on the same line, because pressure inhibits oil vaporization and leads to more coking and cracking reactions at the same heating rate.
results27−29,34 and a few unpublished results from Red Leaf Resources. Shell workers in various publications34 and patents27 noted that oil yields obtained at very low heating rates are higher than those predicted by a linear extrapolation of the data from the work of Campbell et al.15 for heating rates of 1 °C/h and higher. Other experiments and models from LLNL had also predicted that the yield would level off as the cokable components were depleted.2,3,16,23 With the addition of yields from Red Leaf experiments, this sigmoidal behavior becomes exceedingly clear, as shown in Figure 8. The 27-atm results support the notion that readily cokable components are mostly consumed for a heating rate of 1 °C/h. The solid correlation line is a simple function of heating rate: ⎡ ⎛ HR ⎞⎤ ⎟ Yield (vol % FA) = 80 + 20⎢1 − exp⎜ − ⎝ 60 ⎠⎥⎦ ⎣
Figure 10. Effect of externally supplied purge gas on oil yield when oil coking occurs under isothermal conditions13 and at a constant heating rate.15
on oil yield from Stout et al.13 and Campbell et al.15 A higher flow rate is needed at 400 °C, presumably because the rate of oil generation is faster. The purge-gas effects at 5 °C/h are similar to those at 400 °C, even though the maximum oil generation rate is observed at 375 °C. For reference, Campbell et al.15 noted that a purge-gas flow rate of approximately one reactor volume per minute eliminates oil yield loss at 5 °C/h. One can add a term to the effective activation energy to counterbalance the effect of generation temperature on oil vaporization with the effect of purge gas. Gas is cogenerated with oil, and it helps vaporize the generated oil, so one might conceive that the relevant scaling factor for an external purge gas is its ratio to the internally generated noncondensable gases. Any function using this scaled flow rate should eliminate the temperature adjustment term at a high external flow rate. Consequently, a function was derived that reduced that term to zero at an infinite scaled (dimensionless) flow rate. Functions were explored that multiplied the vaporization adjustment term by either exp(−F) or 1/(1 + F), where F is the dimensionless flow rate, and both had the same effect within what is known
0.5
(6)
where HR is the heating rate (in °C/h), FA the Fischer Assay, and vol % FA the ratio of the volumetric yield at the given heating rate to the volumetric yield for Fischer Assay. Also note that the 27-atm data falls on a lower curve than the atmospheric pressure results. This is due to the additional coking and cracking reactions that occur at the same heating rate that are needed to develop equivalent oil volatility to overcome the back pressure. Not all thermal histories can be approximated by a constant heating rate. Consequently, Figure 9 shows the conversion of eq 6 to a function of the midpoint of oil generation temperature, compared to the isothermal yields of Stout et al.38 and Miknis et al.39 The agreement is good to within a few percent and suggests that the yield can be estimated for any thermal history by the time spent at any given temperature. The yield loss in Figure 9 corresponds to the difference 7161
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Figure 11. Calculated excess residence time of generated oil in the pyrolysis region prior to vaporization, as a function of external flow rate for isothermal (left) and constant heating (right) conditions.
Figure 12. Relationship between effective liquid-phase residence time and reciprocal temperature. The left figure compares calculations for isothermal and constant heating rates for F = 0. The right figure shows the same relationships without distinguishing between isothermal and heating rate experiments.
liquid-phase residence time increases faster than the coking rate constant decreases, which is why intraparticle coke formation is greater at lower pyrolysis temperatures. If the activation energy for alkane cracking is in the 55−60 kcal/mol range, cracking would also increase at lower heating rates, but not nearly as fast. Figure 13 shows a qualitative fit of the coking kinetics to the data in Figures 8, 9, and 10. The composite coking and cracking rate constant is given as 4 × 1011 exp(−33780/(RT)) s−1. One can now use these relationships to estimate the effect of gas purge rate on oil yield data from the works of Stout et al.13 and Campbell et al.15 The first step is to estimate the average internally generated gas flow rates over the oil generation window. The Fischer Assay gas yield is approximately
experimentally. Consequently, most effort was applied to calibrating the following equation: Eeff = Etrue +
5[1 − (T /500°C)]2 1+F
(7)
where E and T have the previously specified units and F is dimensionless. For F = 0, eq 7 reduces to eq 4. A parametric study of eq 7 was conducted for various temperatures and heating rates, as shown in Figure 11. The ordinate is the summation over time of the product of the time step and the difference between the generation and vaporization curves, which is an estimate of the excess residence time of the oil as inhibited by vaporization at lower pyrolysis temperatures. As the external flow rate increases, the excess residence time declines. The dimensionless purge-gas flow rate is roughly the external purge rate divided by the average generation rate of noncondensable gases from pyrolysis, so the effect of purge gas in ordinary gas flow rate units changes with pyrolysis temperature and heating rate. At a fixed dimensionless flow rate, the effective liquid-phase residence time, as a function of temperature, can be analyzed in an Arrhenius fashion, as shown in Figure 12. One finds that the apparent “inverse activation energy” for liquid-phase residence time (not rate) is approximately −74 kcal/mol and is roughly independent of F. The pre-exponential factor is approximately (1 + F) × (1.3 × 10−25). If the activation energy for oil coking is ∼35 kcal/mol,15 as the pyrolysis temperature decreases, the
Figure 13. Relationships among oil yield, pyrolysis temperature, and dimensionless flow rate. 7162
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Energy & Fuels proportional to grade, having a value of ∼1500 cm3 gas/100 g shale for 25 gal/ton oil shale.40 Given that oil generation occurs over a period of ∼10 min, the average gas flow rate is 150 cm3 gas/min/100 g shale. Huss and Burnham reported a peak total pyrolysis gas flow rate of ∼25 cm3/min/100 g shale at a heating rate of 2 °C/min for 25 gal/ton Green River shale. At slower heating rates, the situation becomes more complicated. The amount of gas generated during pyrolysis is a function of coking and cracking, approximately doubling between the Fischer Assay and slow heating conditions. Furthermore, the internally generated flow rate is not constant, while the external purge is, so this scaling can only be semiquantitative. The relevant internally generated average gas flow rates are ∼0.05 cm3/min at 350 °C, ∼1.2 cm3/min at 400 °C, and ∼0.5 cm3/min at a heating rate of 5 °C/h. These were estimated by neglecting the increase in gas yield with oil yield loss, taking the relevant gas generation rate to be half the initial value for isothermal conditions and half the peak rate for constant heating, and scaling the peak rate with heating rate. The estimated value at 5 °C/h is approximately half that observed for Garden Gulch shale at a heating rate of 2 °C/h,29 which gives an indication of the approximations involved. Dividing the experimental flow rates by these estimates gives Figure 14,
Figure 15. Correlation of API gravity of shale oil with heating rate.
Figure 16. Correlation of API gravity with H/C ratio of the evolved shale oil.
olefin content, but at the low temperatures associated with low heating rates, the primary cracking products are alkanes. The correlation of gravity with H/C ratio is not as tight as that observed with heating rate, because heteroatom content also plays a role. Differences in measurement temperature may also be a factor, since the measurement temperature is not always reported. Consequently, only a qualitative correlation line is shown. Although the nitrogen content decreases with more coking at slower heating rates, the nitrogen content of the Fischer Assay oil can vary by up to a factor of 2, depending on the location of the interval or zone of the Green River Formation from which the shale is taken.29 The dependence of the sulfur content on heating rate and yield is unclear, and the sulfur content in Fischer Assay oil from different basins or zones within the formation can vary by a factor of 5.41 Although less information is available on distillation profiles for laboratory-based oils, they are available for a wider range of shale oils. Figure 17 shows the relationship between the 50% distillation temperature and the API gravity, including oils from large-scale retorts reported in the Cameron Engineers Synthetic Fuels Data Handbook42 and from oils generated in a highpressure autogenous atmosphere batch reactor.29 Clearly, boiling-point distribution is the primary controlling variable for gravity, and the elemental composition is largely determined by the same coking and cracking conditions that lead to a lighter boiling-point distribution. One can also predict shale oil properties from the volumetric yield of shale oil from an atmospheric pressure reaction in the absence of combustion. Correlations with API gravity and H/C ratio are shown in Figure 18, along with the fraction of organic carbon converted to char (coke). Some of the scatter is due to
Figure 14. Effect of scaled purge-gas flow rates on the retort oil yield from small particles.13,15
which also shows the isothermal curves calculated using eq 5. Comparing these results to the unscaled flow rates in Figure 10, it is apparent that the relative effectiveness of the gas purge switches when using the dimensionless flow rate. More scaled gas purge must be used at 350 °C than 400 °C, most likely because of the lower vapor pressure at 350 °C. The purge-gas effects at 5 °C/h are similar to those at 400 °C, even though the maximum oil generation rate is observed at 375 °C.
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EFFECT OF HEATING RATE ON OIL QUALITY Ryan et al.34 correlated API gravity from various workers with heating rate during pyrolysis. Data from this and other sources are plotted in Figure 15, and it is evident that the gravity of the oil in the absence of a purge gas can be predicted from the heating rate to an accuracy of ∼2°. The AMSO BART data29 are included in the plot but not in the regression analysis, because the Fischer Assay oil of the Garden Gulch Member has a tendency to have a higher API gravity than from the Mahogany Zone. The change in API gravity is due to changes in the molecular composition of the oil. One effect appears in the H/C ratio, as shown in Figure 16, which increases with coking of heteroaromatics and cracking of large alkanes to smaller alkanes. One might expect that cracking would increase the 7163
DOI: 10.1021/acs.energyfuels.5b02026 Energy Fuels 2015, 29, 7156−7167
Article
Energy & Fuels
deduce that the nitrogen content will be reduced by half over this yield range, the pour point will decrease to near room temperature, and the gas-to-oil yield ratio will approximately double. One can also use these relationships in reverse for evaluation of underground pilot tests where the fractional yield cannot be determined directly. The relationships among char yield, oil gravity, and oil yield in Figure 18 define a gas-to-oil ratio, presuming organic carbon balance and knowing the fraction of organic carbon converted to oil in a Fischer Assay and how the carbon content in the oil changes with yield. The average conversion of organic carbon to oil is ∼70%, and the carbon content in the oil is constant at ∼85%, because the increase in hydrogen content is roughly balanced by a decrease in heteroatom content as the yield decreases. These inputs were used to calculate the interrelationships shown in Table 3. From Table 3, the following relations can be derived for up to 20% yield loss:
Figure 17. Dependence of API gravity on distillation temperature of the shale oil.
Gas yield (% RSOC) = 9.00 + 0.2574(100 − vol % FA) − 0.0025(100 − vol % FA)2
(8)
Gas‐to‐oil ratio = 0.13 + 0.0053(100 − vol % FA) + 0.000036(100 − vol % FA)2
(9)
where % RSOC is the percent of raw shale organic carbon that is converted to the specified product. At 20% volumetric yield loss, the char and gas yields increase to 34% and 13%, respectively, and the gas-to-oil ratio increases from 0.13 to 0.25. In addition, the gas-to-char mass ratio from oil yield loss is ∼0.40 for low oil-yield loss and decreases to ∼0.32 at 20% yield loss, with a typical value of 0.36 at ∼10% yield loss. This confirms earlier conclusions that the dominant yield loss mechanism at atmospheric pressure is oil coking, i.e., the conversion of oil primarily to char.15 Slightly different correlations would result if the C5−C9 components in the gas were included in oilthey comprise ∼2% of the raw shale organic carbon in the Fischer Assay gases and ∼5% at heating rates of a few °C/h.40 Also noteworthy is the fact that the char H/C ratios listed by Stout et al.13 and Campbell et al.15 are high because of the inclusion of hydrogen associated with inorganic minerals. When the correlation between gravity and yield in Figure 18 is used to construct a relationship between wt % and vol % yields, an interesting observation emerges. All autogenous experiments at atmospheric pressure from LLNL, AMSO, and Red Leaf fall on the same curve (this is not a direct fit!), as shown in Figure 19, but gas purge and elevated pressure cause slight but reproducible deviations in opposite directions. Part of the reason may be the effectiveness of oil condensation in the presence of purge gases. Another reason may be the effect of purge gas and pressure on olefin yields. Gas dilution increases olefin concentration,43 and increased pressure decreases the olefin content by autogenous hydrogenation.29 Alkenes are typically 1.5% more dense than the corresponding alkane, which corresponds to 1.8° API, but only a portion of the oil falls into that category. More likely, some heavy species are more effectively vaporized by a constant external purge than the self-generated purge. Up to 10% more yield than the Fischer Assay is possible from small particles with an effective purge, but there is no information in the literature that has examined such subtle variations in oil composition.
Figure 18. Correlation of oil H/C ratio, API gravity, and kerogen char yield with volumetric oil yield.
the shale sample used in most of the experiments reported by Stout et al.13 and Campbell et al.,15 having a lower-than-average char yield. From various publications,13,15,16,29 one can also 7164
DOI: 10.1021/acs.energyfuels.5b02026 Energy Fuels 2015, 29, 7156−7167
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Energy & Fuels
Table 3. Inter-relationships among Various Oil and Gas Yields Calculated from Equations in Figure 18 and the Assumption of 70% and 21% Initial Conversion of Kerogen Carbon to Oil and Char oil yield oil yield loss (vol % FA)
API gravitya
relative densityb
0 4 8 12 16 20
22.5 24.3 26.2 28.0 29.9 31.7
1.000 0.988 0.977 0.965 0.934 0.944
(wt % FA)c (wt % RSOC)d 100.0 94.9 89.9 85.0 80.2 75.5
70.0 66.4 62.9 59.5 56.1 52.8
char yield (wt % RSOC)e
gas yield (wt % RSOC)f
gas/oil
gas/char
21.0 23.6 26.2 28.8 31.4 34.0
9.0 10.0 10.9 11.7 12.5 13.2
0.129 0.150 0.173 0.197 0.222 0.249
0.390 0.374 0.366 0.350 0.335 0.320
a
Data taken from Figure 18. bData taken from API gravity. cAs calculated from columns 1 and 3. dData taken from column 4. eData taken from Figure 18. fAs determined by difference.
While the oil liquid remains in the pyrolysis region prior to vaporization and production, it undergoes secondary coking and cracking reactions, which leads to more noncondensable gas, a lighter oil product, and less char (coke). There is adequate information in the literature to develop correlations for this shift in product slate, and some were reported in this paper. They agree reasonably well with previous correlations developed from single sets of experiments. An external purge gas aids oil vaporization from small particles, thereby leading to vaporization at a lower temperature and a higher yield of heavier oil, less gas, and less coke. Less information is available on the effect of such a purge gas at various temperatures and space velocities, but a provisional correction to the effective activation energy has been proposed to account for this effect. It predicts the qualitative trends observed in various literature experiments. Regardless of the limitations of this algorithm, the same relationships between oil yield and oil quality parameters appear to hold, except that oils produced with a gas purge have a tendency to be slightly heavier than those without a gas purge at the same yield. Commercial-scale oil shale processes typically use particles up to at least several inches in size. For indirect heating, the kinetics and yield correlations should apply to these processes directly. For direct heating (hot gas injection), a method would be required to calculate the effectiveness of purge gas as a function of particle size due to diffusion limitations. Literature data show that purge gas does not affect the oil yield from 6 in. cores.44 As the pressure in the pyrolysis vessel increases, the residence time in the liquid and gas phases increases, and the contribution of coking and cracking at a given temperature will be greater. At heating rates of >100 °C/h and temperatures of >420 °C, the primary increase in yield loss would be from coking, since the net amount of coking is relatively small under those conditions. However, for heating rates of
