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The comparison of different kinetic models for heavy oil oxidation characteristic evaluation Wanfen Pu, Yafei Chen, Yibo Li, Peng Zou, and Dong Li Energy Fuels, Just Accepted Manuscript • DOI: 10.1021/acs.energyfuels.7b02256 • Publication Date (Web): 26 Sep 2017 Downloaded from http://pubs.acs.org on September 28, 2017
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The Comparison of Different Kinetic Models for Heavy Oil Oxidation Characteristic Evaluation Wanfen Pu†, *, Yafei Chen†, *, Yibo Li†, Peng Zou†, and Dong Li‡ †. State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, Chengdu 610500, People’s Republic of China ‡. Jiangyou Xingshu Petrochemical Co., Ltd., Jiangyou 621716, People’s Republic of China
ABSTRACT Despite many studies of heavy oil oxidation characteristics, kinetic mechanisms with the comparison of different kinetics models are not well understood owing to the complexities of oil components and non-isothermal oxidation process. Moreover, it is urgent to further evaluate the feasibility and accuracy variations of different kinetic models to optimize the kinetic model for specific situations and purposes. Therefore, thermogravimetry
(TG-DTG)/differential
scanning
calorimeter
(DSC-DDSC)
thermograms under different heating rates were comprehensively studied in this work to elucidate the non-isothermal oxidation behavior with the heating rate influence. Then based on the comparison analysis of model-fitting and model-free methods, the comparisons of kinetic parameters, reaction order, and activation energy distribution were evaluated. And the results indicated the non-isothermal oxidation kinetics parameters varied with the reaction orders and kinetic models. Besides, an obvious increase of LTO activation energy was resulted from the negative temperature coefficient (NTC) effect. Moreover, the preferable kinetic model is ascribed to the specific analysis purposes, as well as the acceptable accuracy of calculated result and the model practicability.
Keywords: heavy oil; non-isothermal oxidation; thermal analysis; oxidation mechanism; kinetic model; heating rate
1. INTRODUCTION Compared with conventional crude oils, how to preferably unlock more trapped heavy
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oil, with the physical and/or chemical upgrades, has placed great pressure and urgency on the researchers and oilfields. As a promising thermal recovery method, In situ combustion (ISC) could activate heavy oils by the heat generation in the combustion front, which is formed and sustained by the burning of deposited fuel with injected air or contained oxygen gas.[1,
2]
During the ISC, there are numerous parallel and
overlapping chemical reactions simultaneously between the crude oil and the oxygen, which make it complicated to acquire detailed and comprehensive understandings on specific reaction paths and resultants, the interaction among the compositions, the evolution procedure from partial oxides to coke deposition, and the oxidation kinetic characteristics corresponding to different temperature intervals.[3-8] In addition, the coking and cracking reactions for non-volatile and thermal stable components, such as heavy asphaltenes and partial oxides, could result in two contrary purposes. The former increases the amount of coke, which is in favor of ISC process. While the latter improves the quality of the heavy oil with lighter hydrocarbon generation.[7, 9, 10] Under this background, thermo-analysis techniques had been employed and are considered as effective tools to determine oxidation characteristics of the crude oil, such as compositions, thermal effect, decomposition characteristic, oxidation mechanism, kinetic analysis, etc.[11-13] As the first thermal analysis tool (DTA) used in crude oil characterization, three oxidation regions, low temperature oxidation (LTO), fuel deposition (FD), and high temperature oxidation (HTO), were recognized in differential thermal analysis (DTA) curve, which was consistent with the latter studies by Kok with differential scanning calorimeter (DSC) and thermogravimetric analyzer (TGA).[12, 14] Vossoughi et al.[4] proposed a kinetic model for the in-situ combustion process based on the combination of TGA and DSC data, which presented satisfying forecast results on fuel deposition with combustion tube experiments. Using DSC and thermogravimetry (TG-DTG), detailed oxidation behaviors of heavy oil alone and with clay additives, and relevant kinetic mechanisms were analyzed by Kok.[12, 15-17] In order to simulate heavy oil oxidation under real high pressure condition, pressurized
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differential scanning calorimeter (PDSC) was employed to investigate the influence of oxygen partial pressure on heavy oil combustion, and it was presented that heat flow peaks became more violent and shifted to lower temperatures owing to the positive influence.[18] However, owing to the composition complexities of crude oil and the limitations of the thermogravimetry methods to reflect the real reservoir conditions, there is still left behind some margin and key information on oxidation mechanisms to be further explored. As the epitome presented in previous literatures, various versions of kinetic models under different assumptions, integral/differential forms, and reaction orders have been evolved and introduced to crude oil oxidation, coupled with thermal analyses, which are mainly classified into isoconversional and non-isoconversional methods.[15, 19-25] The isoconversional method, namely model-free approach, assumes the conversion function f(α) is independent on the variation of heating rates, avoiding inaccuracy associated with the analytical approximation of temperature integral. For the nonisoconversional method, specific reaction model is chosen and the rate constant k(T) is dependent of the Arrhenius temperature, by which a clean separation is difficult to acquire between the temperature related k(T) and reaction model f(α).[20, 24] In order to evaluate the combustion possibility of dry sewage sludges, a good linear regression was gained by the derived Arrhenius model and it was presented that the surface area and pore size must be relative to the activation energy.[22] Kok et al.[3, 15, 16] investigated oxidation behaviors of crude oil and biodiesel samples by Arrhenius, Kissinger, Ozawa-Flynn-Wall (OFW), Kissinger-Akahira-Sunose (KAS), Coats and Redfrn (C-R) methods with the same assumption of first-reaction order (n=1), indicating that the peak and interval temperatures shifted higher with weaker sensitivity as the heating rate increased. Naushad et al.[21] explored thermodynamic parameters in consideration of the variation and relation of free energy change (∆G), enthalpy change (∆H), and entropy change (∆S) based on Van’t Hoff equation. However, the kinetic model with popular first-reaction order, in a way, makes it less accurate to characterize
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the crude oil oxidation involving successive but overlapping reactions, in addition to the un-consistency between the thermogravimetry experiment condition and firstreaction order assumption.[12] In consideration of better kinetic analysis, kinetic methods coupled with reaction order n≠1 have been discussed and even compared with the Arrhenius method (n=1).[11, 26, 27] Whereas it is still essential to compare model-free methods with model-fitting methods to evaluate heavy oil oxidation process, especially for the reaction order variation and activation energy distribution under different conversion rates. However, how to optimize the kinetic model for heavy oil oxidation is still one of the major obstacles to well understandings of oxidation mechanisms and kinetic characteristics. Therefore, in this work, the non-isothermal oxidation characteristic of the heavy oil under multiple heating rates were comprehensively studied using modelfree and model-fitting methods to evaluate the kinetic characteristic contrastively. First, TG/DTG and DSC/DDSC thermograms of the crude heavy crude oil under various heating rates were respectively accomplished to analyze the non-isothermal oxidation mechanism and corresponding heat enthalpy. Furthermore, the influence of heating rate on the oxidation process, heat enthalpy and conversion rate were comprehensively studied with the sigmoidal fitting for the conversion type. Then, the merits and demerits of kinetic models were respectively analyzed via the specific introduction and comparison of kinetic models. Based on theory analysis, the detailed evaluation and comparison of oxidation kinetic characteristic of the heavy oil were investigated with different kinetic models coupling with different reaction orders, n. In addition, the preferable kinetic model was depended on the analysis intention variation and practical situation.
2. EXPERIMENTAL SECTION 2.1. Materials The studied heavy oil was from a block of Tahe oilfield (Tarim Basin, China). This deep reservoir is a carbonate reservoir with the formation temperature and pressure of 120°C
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and 45MPa respectively.[28] The viscosity-temperature curves of targeted heavy oils were measured by the rotational rheometer (MCR 302 Anton Paar, Austria), shown in Figure 1, In addition, the essential physical properties, specific SARA components (eluting chromatography method, ASTM D2549), and element analyses (Elementar, Vario EL Ⅲ) of studied heavy oil samples were tabulated in Table 1. Table 1. Physical properties and SARA analyses of the studied heavy oil sample Viscosity
SARA composition/(wt%)
API°
Element analysis/(wt%)
/(mPa·s, /(20°C) 16.4
120°C)
S
A1
R
A2
C
H
O
N
S
H/C
2650
42
17.5
16.9
23.6
81.9
10.695
4.31
0.48
2.56
1.567
Notes: S-saturates, A1-aromatics, R-resins and A2-asphaltenes. 120 Crude heavy oil Linear fitting
3.8 3.6
黏度/Pas Viscosity/Pas
100
Viscosity/Pas
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80
3.4 3.2 3.0 2.8 2.6
60
90
95
100
105
110
115
120
Temperature/° 温度/°C C
40
y=3.182+123871.84e-0.145x R2=0.977
20
0 40
50
60
70
80
90
100
110
120
Temperature/°C
Figure 1. Viscosity-temperature curve of crude heavy oil measured by the Anton Paar rheometer
2.2. Non-isothermal Thermogravimetric Analysis NETZSCH STA 449F3 PC/PG with DSC and TG-DTG modules was employed to analyze the thermal behavior of the crude heavy oil in air atmosphere from ~30°C to 650°C under air flow (50ml/min) condition. Before the experiments, the cell and temperature calibrations for the DSC system were respectively with sapphire and indium as the reference standard. The TG/DTG system was calibrated with calcium oxalate monohydrate for the temperature readings and silver was used to eliminate buoyancy effects. In addition, based on the recommendation of International Confederation for Thermal Analysis and Calorimetry (ICTAC) committee, each kinetic analysis based on experiment should be accomplished at multiple heating-rates.[19] The
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samples (~20mg) were prepared based on the ASTM standards (D2013-72) and respectively performed with constant heating rates of 5, 15, and 25K/min. And all experiments were performed twice to verify the repeatability with the absolute error, 5%.
3. KINETIC THEORY Since the crude oil is proposed as a complex mixture of hydrocarbons and nonhydrocarbons, which presents various chemical and physical properties for different species, it is more responsible and persuasive to explore and evaluate the heavy oil oxidation process and kinetic mechanism with the utilization of multiple kinetic analysis methods to shrink the deviation and drawback of specific kinetic method hypothesis. In addition, the screening of reaction order was taken into account to better kinetic results. 3.1. Coats-Redfern Method As a popular non-isothermal model-fitting method in integral form, Coats-Redfern (CR) method adopts a single heating rate and various conversion functions, by which the oxidation mechanism along with the activation energies and pre-exponential factors can be obtained.[29] In addition, the optimal reaction order can be determined based on the accuracy comparison of linear fittings. The attractiveness of C-R method is attributed to the ability of direct kinetic parameter acquisition under single heating rate. While the controversy of C-R approach resides in its advantage, namely, it may be non-unique or indistinguishable to only evaluate a single TG/DTG curve to obtain the kinetic triplet, owing to the high correlation degree between α and dα/dt.[30] The calculation of kinetic parameters by thermogravimetry is based on the eq 1. d dt k T f ( )
(1)
Where k is the reaction rate constant, f(α) is the reaction rate function, α is the conversion rate. Generally speaking, the crude oil oxidation is often regarded as a lumped reaction to represent all the components undergoing LTO, FD, HTO stages. And the overall rate of
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crude oil oxidation is relied and obtained by the specific rates of all elementary oxidation reactions. But no obvious limitations among specific reactions, and three major reaction stages indicate that it is more reasonable to consider the variation of reaction order (n) rather than directly setting n=1. Hence, the reaction rate function, f(α), could be expressed as following. f ( ) (1 ) n
(2)
Then, assuming that β is the heating rate,
dt dT
(3)
In addition, combining the Arrhenius theory and integral process, the final style of Coats-Redfern method can be available.[29, 31] 1 (1 )1 n AR 2 RT E ln ln (1 ) ,n 1 2 E RT E T (1 n)
(4)
AR 2 RT E ln(1 ) ln ln (1 ) ,n 1 2 T E RT E
(5)
Based on TG curve under a single heating rate, a straight line with the slop E R and ln(1 ) ln 2 T
the intercept of
ln AR E
1 ln(1 )1 n ln 2 T (1 n)
versus 1/T. In addition, the potential heavy oil oxidation
is yielded by the plot of
or
mechanism could be reflected via the preferential linear correlation model of conversion function. 3.2. Distributed Activation Energy Method As a widely used model-free method to analyze complex reactions, the distributed activation energy method (DAEM) assumes that a number of parallel, irreversible and first-order reactions with different activation energies simultaneously occur. In addition, the activation energy had a continuous distribution function f(E) with the same A0 at the same conversion rate.[32, 33] In order to improve the accuracy of the distribution function with proper mathematical
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expression to meet the assumption, there have been many derivations focused on the thermal decomposition/pyrolysis process of different biomasses, including coal and petroleum products. Whereas it is seldom involved in heavy oil oxidation process, in which numerous and parallel first-order reactions, based on Arrhenius theory, are contained and make it is feasible and reasonable to employ the DAEM method. The DAEM method allows for unmistakably detecting multi-step kinetics as a dependence of the activation energy on the conversion extent. Furthermore, the dependence of activation energy on conversion not only promotes to disclose the complicated oxidation process, but also recognizes the corresponding oxidation kinetic mechanism. The dependent, consecutive, and irreversible oxidation reactions could be identified from the shape and trend of the Eα-α interrelation curve.[34, 35] Whereas some inborn disadvantages of model-free methods are that the alleged “model-free” is deceptive owing to the neglect or delay of f(α) in the kinetic analysis, in which the kinetic triples are thought to be independent of each other with less accurate description of kinetic characteristic. Furthermore, if the condition in the process could be reasonably deem to multi-step kinetics, a multi-step kinetic analysis yielding individual reaction model and a pair of Arrhenius parameters can be accomplished by using model-fitting method rather than model-free method.[19, 36] For the non-isothermal oxidation process of the crude oil with DAEM method, mass variation in the oxidation process, w, against time, t, can be expressed as: t w E 1 exp( A exp( )dt ) f E dE 0 0 w0 RT
(6)
Where w0 is the effective mass loss of the crude oil, f(E) is defined as the activation energy distribution curve representing the differences in the activation energies of many reactions, and A is the frequency factor corresponding to the E value. In addition, it is obviously obtained that the activation energy distribution function f(E) is in accord with the following equation.
0
f ( E)dE 1
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(7)
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In order to evaluate f(E) and A(E), Miura et al[33] had proposed differential and integral methods to simplify the DAEM calculation without assuming A0 value and functional form for f(E) under various heating rates. And the more accurate integral method without tedious differentiation steps is evolved as:
ln
w E AR ln ln ln 1 T2 E w0 RT
(8)
Further, based on the step approximation function theory, a more simplified form can be listed as:
E AR ln 2 ln 0.6075 RT T E
(9)
Using this equation, both activation energy E and frequency factor A0 can be estimated from the Arrhenius curve of β/T2 at the given w/w0 and β values, in which three or more heating rates are usually used. 3.3. ASTM E698 Method Other than kinetic analysis methods mentioned above with TG/DTG curves, the ASTM E698 method developed by ASTM committee for oxidation reactions was preferred to determine the kinetic parameters with DSC curves.[37] In addition, in combined with OFW method or Kissinger method, an intermediate position, between model-fitting and model-free methods, is presented for the ASTM E698 method.[35] In particular, the model, used to estimate the activation energy, is evolved from OFW method in ASTMⅠ method, and from Kissinger method in ASTM-Ⅱ method.[37] For both ASTM models, the reaction rate is assumed to be constant with the zero-order reaction, while the Arrhenius constant is dependent on the reaction medium.[37, 38] The accuracy and feasibility of ASTM method is determined by fundamental methods derived from the ASTM model. The ASTM prediction is seem to present intermediate accuracy between model-fitting and model-free methods. In addition, significantly less accuracy for the ASTM method limits its application in isothermal oxidation prediction, compared with model-free method.[35]
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In ASTM-Ⅰ method, the reciprocal of reaction peak temperature, Tp , is plotted as a function of the log of respective heating rate and apply a layouts, activation energy could be calculated by the following equation.[37, 38] 1 2.303R E d log d D Tp
(10)
In eq 10, if we define x E RT , the D can be then obtained with the assumption that: p x
x
D
exp( x) dx x2
d ln p( x) dx
(11)
(12)
In above equations, the p(x), known as the temperature integral, is derived from the isoconversional methods. Obviously, the temperature integral does not have an exact analytical solution in closed form but can be approximated via an empirical interpolation formula proposed by Doyle.[30, 39] Besides, the value of D is also affected and determined by the range and actual value of x, for example, Doyle’s approximation is more exact for x>20, while Flynn approximation is more exact for x
