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Heat release model for the low temperature oxidation of heavy oils from experimental analyses and numerical simulations Hang Jiang, Junyu Yang, Jia Huang, Weifeng Lv, Junshi Tang, Qianghui Xu, Yunchao Han, and Lin Shi Energy Fuels, Just Accepted Manuscript • DOI: 10.1021/acs.energyfuels.8b04506 • Publication Date (Web): 01 Apr 2019 Downloaded from http://pubs.acs.org on April 3, 2019

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Heat release model for the low temperature oxidation of heavy oils from experimental analyses and numerical simulations Hang Jiang1, Junyu Yang2, Jia Huang1, Weifeng Lv1, Junshi Tang1, Qianghui Xu2*, Yunchao Han2, Lin Shi2 1 State Key Laboratory of Enhanced Oil Recovery, Research Institute of Petroleum Exploration & Development, China National Petroleum Corporation, Beijing 100007, China 2 Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Department of Thermal Engineering, Tsinghua University, Beijing 100084, China *Corresponding Author E-mail address: [email protected]

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Abstract

Low temperature oxidation (LTO) of heavy oils involves many complex reaction mechanisms that are important for the success of ignition and front propagation during in situ combustion (ISC). In this study, experiments and numerical simulations were combined to investigate the heat release characteristics of LTO. Pressure differential scanning calorimeter (PDSC) experimental analyses were used to measure the heat release for various heating rates and pressures under temperatures from 50 to 350°C. The heat release curves for the various heating rates were consistent with a theoretical Arrhenius analysis, indicating the feasibility of simulating the heat release during the LTO reaction by an Arrhenius equation. The pressure also had a significant effect on the LTO heat release. The results show that the total amount of heat release from LTO is positively correlated with pressure but that the oil consumption rate did not change. A numerical model was used to simulate the PDSC experiments to study the LTO reaction kinetics based on an exothermal Arrhenius reaction model to calculate the heat release rates. The kinetic parameters were obtained using the history matching method with different reaction enthalpies at different pressures to model the effect of pressure on the heat release. The reaction model and kinetic parameters successfully predicted the LTO heat release rates; therefore, these parameters are valuable tools for engineering applications.

Keywords In situ combustion; low-temperature oxidation; pressure differential scanning calorimeter; Arrhenius equation


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1. Introduction Heavy oils with high viscosities and densities at reservoir conditions constitute a substantial amount of the world’s oil resources.1 Enhanced oil recovery (EOR) methods are commonly used to extract such oils. In situ combustion (ISC) is a promising thermally enhanced oil recovery technique in which thermal energy is generated inside the reservoir via combustion of the oil with injected oxygen.2 The ISC process can significantly increase oil displacement and achieve in situ upgrading.3 Oil viscosity is reduced significantly under increased temperatures4 and with the consumption of the heaviest fractions in the oil. The oil can then be more easily driven to the production wells. ISC has many advantages, including high recovery efficiency and low cost.5 Greenhouse gases generated by the ISC can be sequestered in the reservoir; therefore, the ISC method also benefits the environment.6 Implementing ISC inside a reservoir has three main reaction zones: low temperature oxidation (LTO), thermal cracking and high temperature oxidation (HTO).7-9 LTO generally occurs at temperatures less than 350°C when the oil reacts with oxygen to produce products with higher densities and viscosities.10 Thermal cracking is a fuel formation reaction that generates coke and low molecular-weight compounds from the LTO product. HTO reactions are carbon bond reactions of oxygen with coke that generate large amounts of heat. The LTO reactions are the most complex and play an important role in the ISC process. The success of the ignition process and the stability of the combustion front are strongly influenced by the LTO reactions;11 therefore, the LTO reactions must be well understood. Various investigations have been performed on the mechanisms for ISC in the laboratory. Li et al.12 used thermogravimetry–derivative thermogravimetry (TG-DTG) and differential scanning calorimetry (DSC) to verify the LTO and HTO temperature interval and the influence of the


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heating rate on the reactions. The DSC data were fit to a model to obtain the kinetic parameters for both LTO and HTO. Gundogar et al.13 investigated the non-isothermal thermal behaviour of six kinds of oil using the TG/DTG and DSC methods, and their data were fit to the Arrhenius and Coats-Redfern models. Yuan et al.14 used DTG analyses to measure the temperature intervals for the three reaction processes and an Arrhenius analysis to obtain the kinetic parameters. Khansari et al.6,7 used the isothermal TG/DTG method to investigate the LTO reaction kinetics with four reaction models developed for different temperature subranges to simulate the experimental data reasonably well. Hu et al.15 compared the DTG curves of oil-only and oil-cuttings to analyse the influence of the solid matrix in oil sands. Kok et al.16,17 combined TG/DTG and Fourier-Transform Infrared (FTIR) spectrometer to obtain the kinetics of oil oxidation and determine the composition of the gaseous products during LTO and HTO. These investigations of the kinetic characteristics provided an understanding of the oil oxidation process and models to predict the ISC reaction behaviour. However, most previous investigations focused on the mass change in the oil oxidation process with the kinetic parameters fit to the conversion rate. The heat release characteristics of the oil oxidation process also need to be investigated since they more directly influence the ISC reaction. Bhattacharya et al.18 used an accelerating-rate calorimeter (ARC) to measure the selfheating rate of heavy oil and simulated the experimental data using a modified kinetics model, and the results were consistent with the measured temperature and self-heating rate data. Although TG and DSC analyses have been widely used to study oil oxidation,12-17,19-24 these analyses can only be performed at atmospheric pressure. Thus, the experimental results cannot accurately reflect the reaction kinetics at typical reservoir conditions. Recent studies have measured the reaction kinetics at high pressures using pressure differential scanning calorimetry (PDSC) analyses to investigate


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the oil reaction rates at high pressures.9,25-26 These studies showed different heat release rates at high pressures than those obtained using traditional DSC analyses. In this work, PDSC analyses were used to measure LTO heating rate data at various heating rates and pressures. A numerical model was then developed to simulate the PDSC results using an exothermic reaction model for the LTO heat release, including the effect of pressure on the heat release rate. The kinetic parameters and reaction enthalpy were calculated by history matching. The results can be used to predict low temperature oxidation release rates for ISC processes. 2. Experimental Section 2.1 Materials A heavy crude oil from the Xinjiang oilfield in China was selected as the oil sample for this study. The reservoir depth is about 500 m with the formation pressure of 4.7MPa and the formation temperature of 22oC. The crude oil properties and the saturate-aromatic-resin-asphaltene (SARA) analysis results are listed in Table 1. The crude oil viscosity was measured using a rheometer (HAAKE MARS Ⅲ, Germany) with the crude oil SARA fractions measured according to the China Petroleum and Chemical Standard SH/T 0509-92. Dehydration and degassing were used to eliminate the effects of water evaporation and steam distillation on the LTO heating rate measurements. 2.2 Experimental Apparatus A PDSC cell (TA Q20P, the USA) was used to measure the crude oil LTO heat flow by subjecting the crude oil to a programmed high pressure and high temperature environment similar to the ISC conditions. The PDSC cell was enclosed in a steel cylinder to provide the calorimetric measurements at elevated pressures up to 7 MPa for temperatures from -130oC to 725°C. Figure 1 shows the schematic diagram of the PDSC device. A backpressure regulator at the outlet was used


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to adjust the reactor pressure with a pressure gauge monitoring the cell pressure. A constant flow rate of up to 200 ml/min was controlled by a Brooks mass flow metre. The tested oil sample and the reference were placed on top of the discs. The difference between the heat flow rates of the sample and the reference was measured using thermocouples. The LTO oxidation behaviour was then characterized by the heat transfer in and out of the oil sample. Table 1. Xinjiang crude oil sample properties API gravity, oAPI

15.9

Viscosity, mPa·s, 50°C

9283

Viscosity, mPa·s, 80°C

819

Saturate, wt%

48.00

Aromatic, wt%

25.27

Resin, wt%

26.15

Asphaltenes, wt%

0.58

2.3 Experimental Procedure A baseline calibration was first recorded to improve the PDSC thermal analysis accuracy by flattening the slope and the offset of the heat flow curve measured with an empty experimental system over the characteristic LTO temperature range of 50-350°C. One milligram each of the tested oil sample and the reference sample was weighed on an electronic balance (Mettler Toledo AL204, Switzerland) with 0.1 mg precision. The samples were then loaded on the discs at ambient pressure. After hooking up all the connections, the air injection was initiated to pressurize the cell to the desired pressure. When the pressure was stable, the thermal analysis was started by setting the air flow rate to 50 ml/min and keeping the heating rate at the desired rate. Thermal analyses


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were run with various pressures and heating rates to investigate the effect of the reaction pressure and the heating rate on the crude oil LTO heat release. To investigate the effect of high pressure, the experiment pressures were selected close to the reservoir condition as 1 MPa, 2 MPa, and 3 MPa. Considering high reaction pressure would increase measurement errors and bring potential safety risks, higher pressure which was closer to the reservoir condition didn’t perform. Different heating rates of 1°C/min, 2°C/min, and 3°C/min were set in the experiment based on previous work27,28. The experiment data of these heating rates was used for kinetics analysis. Inlet Valve Heating Block

Pressure Cell

Sample Pan Air

Thermocouple

Outlet Valve

P Mass Flow Meter

Backpressure Regulator

Figure 1. Schematic diagram of the PDSC device. 3. Numerical Simulation 3.1 Governing Equations and Model Assumptions To further analyse the LTO heat generation characteristic, the PDSC experiments were modelled numerically using the commercial thermal reservoir simulator (STARS, Version 2015.10, CMG).


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The governing equations for each component’s mass balance and the energy balance used in the simulator are as follows:18

(1)

(2) where all symbols are defined in the nomenclature. The convection and diffusion terms for the liquid phases were neglected since the oil sample used in the PDSC experiments was quite small. Thus, the equations were as follows:

(3)

(4) The gas phase flow rate in the energy equation was calculated using Darcy’s law. The K value for the oil phase were set to zero as there was no steam distilling owing to the initial degassing of


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the oil sample. In addition, since there was no oil component in the gas phase due to the absence of distilling, the oil phase mass balance can be further simplified as follows:

(5) where only accumulation and reaction terms are considered. In addition to the governing equations for the mass and energy balances, the calculation also needs a reaction model to simulate the PDSC process. Since the focus of this study is the exothermic character of the LTO reaction, a model was developed to predict the LTO heat generation rate. Using the analyses described in Section 4.1, an exothermic reaction model was used with a reaction rate given by the Arrhenius model:

Oil  a O 2  b LTO Oxide  c CO 2  d H 2 O

dwoil  E  A exp   dt  RT

 n  woil 

(6) (7)

where woil represents the residue oil weight, A is the pre-exponential factor and E is the activation energy. Since the air pressure influences the oxygen concentration, the pressure has a significant effect on the heat generation rate which was considered by adjusting the reaction enthalpy with pressure as described in Section 4.2. 3.2 Numerical Modelling of the PDSC Procedure The PDSC experiments were simulated using a three-dimensional Cartesian coordinate system with 3×1×1 grid blocks as illustrated in Figure 2. The three grid blocks represent the injector, the reservoir and the producer, and the overall size of the grid blocks was 1.5 cm×0.5 cm×0.1 cm. The crude oil reacts with the air in the middle reservoir block. Since the oil sample mass was quite small and sufficient air was injected into the PDSC experiments, the reaction process was treated


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as “zero-dimensional,” which means that the components and temperature were assumed to be uniformly distributed in the oil phase. Thus, the LTO reaction could be simply simulated in one block. The air flow rate was controlled in the injector block by setting the injection parameters in the simulator with a constant flow rate of 50 ml/min to mimic the experimental conditions. The back pressure was adjusted in the producer block to produce the same system pressure as in the experiments.

Figure 2. Grid blocks for the PDSC simulation. The temperature was increased at a constant rate in the experiments. To realize the constant heating rate in the CMG simulator, the grid blocks, which characterized the PDSC cell, were set with a constant heat source, while their specific heat was given a large number to control the block temperature in a ramping way and eliminate the effect of the fluid internal energy change, heat conduction and reaction heat release on the block temperature. Thus, the energy equation only included the temperature variation and source terms:

(8) Different constant heating rates were generated by adjusting the heating source term. The fluid properties were determined by a property calculator (Win Prop, Version 2015.10, CMG) based on measured data. The major parameters required for the simulation model are listed in Table 2. Rock


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porosity and oil saturation were adjusted to meet the oil mass. The relative permeability of the liquid phase was set to zero considering the oil sample keep static in the PDSC process. 3.3 History Matching Method History matching of the prediction with experimental data was used to obtain the kinetic parameters in the reaction model. The reaction enthalpy and the kinetic parameters, including the pre-exponential factor, activation energy and oil reaction order, were selected as the history matching variables. Simulation results using different groups of kinetic parameters were compared with the experimental data to find the optimal parameters using the designed exploration and controlled evolution (DECE) optimization method.29 The algorithm explores the history matching variable search space in a random manner with statistical analyses to find the optimal values. The pre-exponential factor, activation energy and oil reaction order, which are related to the oil consumption rate, were identical for each condition, and the reaction enthalpy was adjusted for different pressures to represent the effect of pressure on the heat release rate. The algorithm flowchart is shown in Figure 3. Table 2. Properties Used in the Numerical Simulations Rock porosity

0.95

Oil Saturation

0.0439

Molecular weight of oil, g/gmol

587

Critical temperature of oil, °C

507.16

Critical pressure of oil, kPa

916.12


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Figure 3. Flowchart for the algorithm combining the experimental data and the predictions 4. Results and Discussion 4.1 Effect of Heating Rate on the LTO Heat Release The PDSC analyses used various pressures and heating rates to measure the heat release rates of heavy oil under a wide range of conditions. The experiments used pressures ranging from 1 to 3 MPa, which were close to the real reservoir conditions. The heat generation rates from the LTO reaction at the various heating rates of 1°C/min, 2°C/min and 3°C/min are shown in Figure 4(a) for a pressure of 2 MPa. The three curves showed similar tendencies. The heat release started at almost the same temperature of approximately 180°C, indicating that the initial temperature of the


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exothermic oxidation reaction did not change with the heating rate. The peak heat generation rates are 3.2 W/g, 5.1 W/g and 7.5 W/g for the three heating rates exhibiting a positive correlation with the heating rate. The temperatures corresponding to the peak points were 261°C, 272°C and 277°C, and these also increased with the heating rate. The peak heat generation rates and the corresponding temperatures in other conditions are listed in Table 3. These peak points also had positive correlation with the heating rates as Figure 4(a) shows. Figure 4(b) shows the heat flow curve given by the Arrhenius analysis.26 For different heating rates, the reaction occurs begins at the same temperature and the peak heat emission and its temperature increase with increasing heating rate. The qualitative characteristics of the Arrhenius analysis were consistent with the experimental results, thus indicating the feasibility of characterizing the LTO heat release rates using the Arrhenius equation described by Eq. 7. At the end of the PDSC process, the heat emission was not zero as in the Arrhenius model due to the initialization of the crude oil high-temperature oxidation, which resulted in differences between the simulations and the experimental data (discussed in Section 4.3). Table 3. Peak Heat Generation Rates and Corresponding Peak Temperature Experiment Conditions

I MPa

3MPa

Peak Temperature

Peak Heat Generation Rate

1oC/min

265oC

2.3 W/g

2oC/min

276oC

4.0 W/g

3oC/min

283oC

5.5 W/g

1oC/min

256oC

3.5 W/g

2oC/min

267oC

5.9 W/g

3oC/min

273.5oC

8.6 W/g


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(b)

(a)

Figure 4. (a) Heat generation curves for different heating rates. T1, T2 and T3 are the temperatures corresponding to the peak heat release rates. (b) Heat release rates predicted by the Arrhenius equation for different heating rates29. 4.2 Effects of Pressure on the LTO Heat Release Pressure is a crucial parameter that influences the LTO heat release rates since the pressure determines the oxygen concentration available for the reaction. The effect of pressure on the reaction was investigated by measuring the heat release rates at various pressure. Figure 5 shows the PDSC heat release curves for air pressures of 1 MPa, 2 MPa, and 3 MPa at the same heating rate of 3°C/min. The data show three peaks with heat release rates of 5.5 W/g, 7.5 W/g and 8.6 W/g. The point where heat release rate reduced to the minimum was considered as the ending of LTO. It can be observed the reactions began and ended at the same temperatures for the three pressures, which suggests that the crude oil was exhausted at the same time for all three cases. Previous thermogravimetry analyses9 at various pressures have shown significant mass losses under LTO when the temperature did not vary with the pressure, which suggests that the LTO reactions were kinetically controlled and the oxygen concentration did not influence the oil consumption rate because excessive air was present. The experimental observations of the same


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LTO temperature range for various pressures in this study are consistent with the previous results. Thus, these results suggest that the crude oil LTO kinetic model described in Eq. 7 is not dependent on the oxygen partial pressure.

(a)

(b)

Figure 5. (a) Heat flow rates and (b) cumulative heat releases for oil samples at various pressures at a heating rate of 3°C/min. The cumulative LTO heat release given in Figure 5(b) was found by integrating the heat release rates over time. The total heat release rates for 1 MPa, 2 MPa and 3 MPa were 7.76 J/g, 9.75 J/g and 10.61 J/g, respectively. Although the oil mass consumption rates for the various pressures had the same characteristics, the LTO heat generation rates were positively correlated with the pressure. Previous work26 proposed that pressure had a great influence on the evaporation of light components. During LTO of heavy oil, light hydrocarbon was produced and then volatilized with the increasing temperature. However, the increasing pressure can suppress the evaporation of the light hydrocarbon and retain them in the liquid phase, resulting in more components participated in the LTO rather than left the reactor with air flow. Therefore, the heat generation increased with the pressure due to more light hydrocarbon included in oxidation, while the total mass consumption including the evaporation and oxidation changed little with pressure according to the previous


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thermogravimetry analyses9. Under this conclusion, different reaction enthalpies should be used for each pressure to represent the effect of pressure on the heat release simulation. 4.3 LTO Reaction Heat Release Model From the experiment analyses in Sections 4.1 and 4.2, the LTO heat release rates were simulated using an overall exothermic reaction model described by the Arrhenius equation with different reaction enthalpies corresponding to different pressures. The kinetic parameters were found by comparing the simulations to the data for the 3°C/min heating rate and the 2 MPa pressure case. Then, the models were compared to the data sets for 1 MPa and 3 MPa to determine the different reaction enthalpies for these two pressures. The other experiment conditions were also simulated to validate the reaction model and the kinetic parameters. The obtained parameters are listed in Table 4. The kinetic parameters for the activation energy, pre-exponential factor and reaction order were the same for all conditions. The reaction enthalpies at different pressures are shown in Figure 6. The increase in the reaction enthalpy is slower at higher pressure because the pressure influenced the heat release by changing the amount of incomplete oxidation products in the gaseous phase. In this case, the reaction enthalpy should increase more slowly at higher pressures as the total heat release reaches a limit when all the products are completely oxidized. Further measurements at additional pressures are required to determine the quantitative relation between the reaction enthalpy and pressure. Table 4. Kinetic Parameters Obtained by History Matching Activation energy, J/gmol

8.25×104

Pre-exponential factor

8.33×108

Reaction order of oil

1.48

Reaction Enthalpy at 1 MPa, J/gmol

4.84×106


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6.47×106


7.20×106

Figure 6. LTO reaction enthalpies for various air pressures. The reaction model was validated by simulations at various heating rates and pressures with the results shown in Figure 7 for various pressures at the 3°C/min heating rate. The predictions are consistent with the experimental data, which indicates that the proposed reaction model and kinetic parameters can successfully simulate LTO reactions. The PDSC process at the 1°C/min heating rate was also simulated to further validate the model. As shown in Figure 8, the predicted heat release rates are consistent with the experimental data before 250 min (when the temperature reached 300°C). Near the end of the PDSC process, the simulations predicted that the heat release would stop, which did not occur in the experimental data. The total measurement time for the 1°C/min case was quite long because of the slow heating rate, and the LTO reactants may have been completely consumed near the end because the oil sample was quite small. Then, the high temperature reaction may have begun near the end stage of the heating process. The long heating time led to more obvious effects of the other reactions, resulting in differences between the


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predictions and the data in the final stage. More research is needed to investigate the effects of other reactions, such as high-temperature oxidation over a wider temperature range. In general, the comparisons indicate that the reaction model can accurately predict the LTO heat release rates.

Figure 7. Measured and predicted accumulated heat generation totals for the 3°C/min heating rate.

Figure 8. Measured and predicted accumulated heat generation totals for the 1°C/min heating rate. In order to further validate the reaction model, two ASTM methods were used to estimate the


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LTO activity energy and compared with the history matching30-32. In the first ASTM method, the temperatures, T, at the heat release peak point and the heating rates,  , were utilized to approximately calculate the activation energy as the following equation33-34.

E =  2.303

R d log10   D d 1/ T 

(9)

In the second ASTM method, the activation energy is approximately calculated as35,

E=

d ln   / T 2  d 1/ T 

(10)

where D is a correction factor related to E / RT . The linear regressions between log  and 2 1/ T , ln   / T  and 1/ T are performed in Figure 9 to obtain the slope as the activation energy.

The calculated activation energy at different pressures are listed in Table 5. The calculated activation energy by ASTM1 and ASTM2 are averagely 14.70×104 and 6.36×104, respectively, while the history matching result, 8.25×104, is right between the two ASTM values. They are comparable with the same order, but with some absolute difference. The approximation in the two ASTM method derivations34-35 are considered to bring in the activation energy difference among the ASTM method and history matching. Table 5 also shows that the activation energy from the ASTM methods almost keep constant with different reaction pressure, further confirming the standpoint that the pressure does not influence the mass consumption rate during the LTO. Table 5. Activation Energy Obtained by ASTM method Experimental Pressure, MPa

1

2

3

Activation energy, ASTM1, J/gmol

14.29×104

15.36×104

14.45×104

Activation energy, ASTM2, J/gmol

6.18×104

6.67×104

6.25×104


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(a)

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(b)

Figure 9. Fitting lines of (a) log 

versus 1/ T ,(b) ln   / T 2  versus 1/ T at different

pressures. 5. Conclusions PDSC experiments were conducted with various heating rates and pressures to investigate the heat release characteristics of low-temperature oxidation of heavy oil. The LTO heat generation curve was consistent with a previous Arrhenius analysis, which indicates that the Arrhenius kinetic model can be used to predict LTO heat release rates. The experiments at various pressures showed that pressure is a significant factor that influences the heat generation but has little effect on the oil mass consumption rate, which was consistent to the previous investigation. The experimental data were used to develop an LTO reaction model based on the Arrhenius equation with different reaction enthalpies for different pressures. The kinetic parameters and the reaction enthalpies were obtained using history matching with the data and verified by ASTM methods. Simulations with the different heating rates and pressures were consistent with the experimental data, suggesting that the reaction model can accurately predict the LTO heat release rates. At higher temperatures,


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other reactions in addition to the LTO reactions began to affect the heat release rates; therefore, the simulations could not accurately predict the data over very long times. Thus, additional reaction models that include the effects of additional reactions at other temperatures are needed. The LTO reaction model and kinetic parameters determined here can be used to predict the heat generation characteristics of ISC at low controllable temperatures in engineering practice when LTO is dominant. Acknowledgements The work was supported by the National Natural Science Foundation of China (No.51876100), the Science Fund for Creative Research Group (No.51621062) and the PetroChina Technology R&D Project on New Technology and Method for Oil & Gas Development (2016A-0901). Nomenclature Cg

average volumetric heat capacity of the gas phase

cgi

compressibility of component i in the gas phase

Co

average volumetric heat capacity of the oil phase

coi

compressibility of component i in the oil phase

Cw

average volumetric heat capacity of the water phase

cwi

compressibility of component i in the water phase

Dgi

effective diffusivity coefficient of component i in the gas phase

Doi

effective diffusivity coefficient of component i in the oil phase

Dwi

effective diffusivity coefficient of component i in the water phase

kg

gas permeability

ko

oil permeability


Energy & Fuels 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

kw

Page 22 of 28

water permeability production rate of component i per unit volume reaction rate of component i per unit volume

Mr

volumetric heat capacity of the rock

MWg

average molecular weight of the gas phase

MWi

molecular weight of component i

MWo

average molecular weight of the oil phase

MWw

average molecular weight of the water phase

Pg

gas phase pressure

Po

oil phase pressure

Pw

water phase pressure reaction energy per unit volume source energy per unit volume

Sg

gas saturation

So

oil saturation

Sw

water saturation

T

temperature

ug

gas phase velocity

Ug

internal energy of the gas phase per unit mass

uo

oil phase velocity

Uo

internal energy of the oil phase per unit mass

uw

water phase velocity

Uw

internal energy of the water phase per unit mass


Page 23 of 28 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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wi

concentration of i in the water phase

xi


yi


g

gas phase viscosity

o

oil phase viscosity

w

water phase viscosity

g

gas phase density

o

oil phase density

w

water phase density



specific gravity



porosity

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[5] Hascakir B, Ross C, Castanier L M, Kovscek, A. Fuel Formation and Conversion During InSitu Combustion of Crude Oil. SPE J. 2013, 18(6), 1217-1228. [6] Khansari Z, Gates I D, Mahinpey N. Detailed Study of Low-Temperature Oxidation of an Alaska Heavy Oil. Energy Fuels 2012, 26(3), 1592–1597. [7] Khansari Z, Kapadia P, Mahinpey N, Gates, I. D. A new reaction model for low temperature oxidation of heavy oil: Experiments and numerical modeling. Energy 2014, 64(1), 419-428. [8] Chen Z, Lei W, Duan Q, Zhang, L, Ren, S High-Pressure Air Injection for Improved Oil Recovery: Low-Temperature Oxidation Models and Thermal Effect. Energy Fuels 2013, 27(2), 780-786. [9] Fan C, Zan C, Zhang Q, Shi L, Hao Q, Jiang H, Wei F. Air Injection for Enhanced Oil Recovery:

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[20] Elbaz A M, Gani A, Hourani N, Emwas A H, Sarathy S M, Roberts W L. TG/DTG, FTICR mass spectrometry, and NMR spectroscopy study of heavy fuel oil. Energy Fuels 2015, 29(12), 7825-7835. [21] Abivin P, Taylor S D, Freed D. Thermal behavior and viscoelasticity of heavy oils. Energy Fuels 2012, 26(6), 3448-3461. [22] Wei B, Zou P, Zhang X, Xu X, Wood C, Li Y. Investigations of Structure–Property– Thermal Degradation Kinetics Alterations of Tahe Asphaltenes Caused by Low Temperature Oxidation. Energy Fuels 2018, 32(2), 1506-1514. [23] Varfolomeev M A, Nagrimanov R N, Samatov A A, Rakipov I T, Nikanshin A D, Vakhin A V, Solomonov B N, Nurgaliev D K, Kok M V. Chemical evaluation and kinetics of Siberian, north regions of Russia and Republic of Tatarstan crude oils. Energy Sources, Part A, 2016, 38(8), 1031-1038. [24] Varfolomeev M A, Nagrimanov R N, Galukhin A V, Vakhin A V, Solomonov B N, Nurgaliev D K, Kok M V. Contribution of thermal analysis and kinetics of Siberian and Tatarstan regions crude oils for in situ combustion process. J. Therm. Anal. Calorim., 2015, 122(3), 13751384. [25] Li J, Mehta S A, Moore R G, Zalewski E, Ursenbach M G, Van Fraassen K. Investigation of the Oxidation Behaviour of Pure Hydrocarbon Components and Crude Oils Utilizing PDSC Thermal Technique. J. Can. Pet. Technol. 2006, 45(01), 48-53 [26] Klinchev V A, Zatsepin V V, Ushakova A S, Telyshev S V. Laboratory studies and implementation of in-situ combustion initiation technology for air injection process in the oil


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