Criteria To Select Operational Variables That Improve the Accuracy of

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Criteria To Select Operational Variables That Improve the Accuracy of the Evaluation of Kinetic Parameters in a Kinetic Cell Used in the Study of In Situ Combustion Sebastian López and Alejandro Molina* Departamento de Procesos y Energia, Universidad Nacional de Colombia Sede Medellín, Medellín, Antioquia, Colombia ABSTRACT: Criteria to operate kinetic cells used in the characterization of the kinetic parameters for the reactions that take place during in situ combustion (ISC) were defined using computational fluid dynamics (CFD). To evaluate the assumption of complete mixing in kinetic cells, CFD simulations of a ramped temperature oxidation (RTO) test for the Athabasca bitumen were carried out. A dimensionless Damköhler (Da) number was particularly defined for ISC tests and used as an indicator of the homogeneity in the kinetic cell. The simulations were developed using ANSYS Fluent 13.0 by a two-dimensional discretization of the domain and several user defined functions particularly designed for the simulation of ISC. The CFD simulations were compared to a zero-dimensional (0D) model used to represent complete mixing conditions. CFD showed concentration gradients along the kinetic cell axis that were minimized when the operational parameters were modified to obtain Da lower than 7, a value that guaranteed that the behavior in the cell approximated that of complete mixing represented by the 0D model. For Da > 7, dispersion was evident and predictions of the CFD and 0D models were different.

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INTRODUCTION In situ combustion (ISC) is an enhanced oil recovery (EOR) process that is part of a group of techniques, usually referred to as thermal recovery methods, where heat is used to improve oil flow. The heat required in ISC comes from burning a portion of the oil. Combustion is sustained by a continuous injection of air or oxygen-enriched air that creates a mobile combustion front. The oil is driven to the producer wells by a combination of the drive by combustion gases and water.1 ISC involves various phenomena, such as chemical reactions, flow in porous media, and heat and mass transfer. While the petroleum community has a century of experience upon dealing with heat transfer and flow in porous media in reservoirs, the complexity of chemistry coupled with mass and heat transfer is something that may represent a challenge. Factors such as porosity, permeability, mineralogy, catalytic effect of some clays in the reactivity of the oil, ISC mode, air fluxes, and ignition strategy may be important in ISC.2−9 The evaluation of the factors previously mentioned has normally been carried out in lab-scale equipment at petroleum engineering research laboratories. The correct use and interpretation of lab-scale results are fundamental in the design of a successful ISC project.10 Laboratory equipment for ISC can be classified, according to the aim of the experiments, in two categories: those designed to determine the reactivity of the oil and the self-sustained temperature and those used to emulate a reservoir to evaluate parameters changing in space, fluid production, and other operational parameters. Those in the first category, mostly of small size, are fundamental in the evaluation of kinetic mechanisms. Kinetic cells are the most common example.11,12 A detailed analysis of the effluent gases is used to infer the kinetics of the chemical reactions in ISC. In the second category, combustion tubes that allow for the estimation of the velocity and the temperature of the © XXXX American Chemical Society

combustion front as well as the percentage of oil recovered are the preferred setup.8,13 One common experiment in a kinetic cell is the oxidation of the oil under a controlled heating rate, known as ramped temperature oxidation (RTO), and normally modeled as a completely mixed reactor, where multiple reactions take place. This technique has been extensively used for developing mechanisms to describe the reactions that take place in the ISC process. Kinetic cells have been modeled as semi-batch reactors,14 where the mixture oil/sand is stationary and air flows through the reactor. However, various researchers observed a combustion front in these setups, which provide evidence of heterogeneities causing different reaction velocities along the cell.15−17 These inhomogeneities can affect the interpretation of the results obtained in a RTO test if the cell is modeled as a perfectly mixed semi-batch reactor. Despite the existence of segregation in the cell, the importance of this effect in the interpretation of the results has not been determined in the referred literature, even though some studies analyzed data with apparent segregation as zero-dimensional (0D).14,18 In this paper, we evaluate the assumption of complete mixing in a kinetic cell by a thorough computational fluid dynamics (CFD) simulation of a RTO test of an Athabasca bitumen.

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MODEL

The simulations were based on results reported by Belgrave et al.16 These authors simulated a RTO test with the mathematical code described by Coats.19 In contrast to the simulation by Belgrave et al.,16 in this study, the kinetic cell was simulated with the commercial CFD Special Issue: In Honor of Professor Brian Haynes on the Occasion of His 65th Birthday Received: September 20, 2016 Revised: November 30, 2016 Published: December 5, 2016 A

DOI: 10.1021/acs.energyfuels.6b02191 Energy Fuels XXXX, XXX, XXX−XXX

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As standard for 0D behavior, a code in the MATLAB software was developed. The system was modeled as a semi-batch reactor, where the only species that enter and leave the reactor are those in the gas phase. The 0D model solves nine differential equations that represent the mass balance of all of the species involved in the process. The boundary conditions used in the simulation were as follows: Inlet: Air (xO2 = 0.21) was at a rate of 0.081 standard m3/h (throughout the paper standard conditions are 1 atm and 298 K). The temperature of the injected fluid was kept constant at 300 K. Wall: The model was programmed to raise the temperature of the wall of the kinetic cell at the same heating rate described in ref 16, at 100 °C/h. Outlet: The pressure was kept constant at 4100 kPa. Axis: The symmetry of the kinetic cell was used to reduce the number of nodes. The kinetic mechanism of Belgrave et al.16 was used in the simulation. The mechanism represents crude oil as a mixture of maltenes and asphaltenes that undergoes two reactions of oxidation at a low temperature, three reactions of pyrolysis, and one reaction of oxidation at a high temperature. The kinetic reaction mechanism as well as the variation of physical properties with the temperature were implemented in the CFD code through UDFs, submodels within the CFD code developed by the authors to model ISC.

software ANSYS Fluent 13.0, via a two-dimensional (axisymmetric) discretization of the domain. While there are other experiments20,21 with smaller cells that could be used to further validate the results of this study, we limited our analysis to the experiments by Belgrave et al.,16 because these authors provided all of the information required for the simulations. In the CFD simulation, four phases were considered: coke (treated as a solid phase), gas, oil, and water, in a multicomponent system based on an Eulerian−Eulerian approach. The model included the interaction of the various phases through the heterogeneous reactions that take place in the process. The rate laws for these reactions were implemented in Fluent with user defined functions (UDFs) that define the rate law using variables of the system, such as saturation, porosity, and molar fractions. A laminar regime was used in the system to represent the flow of the phases through the porous media. UDFs were also developed to represent the relative saturation for the system, liquid−gas and water−oil, and the dependency of some properties, such as viscosity, with the temperature and to express the mixing law for multicomponent systems. Figure 1 shows the initial oil saturation and the mesh used to represent the cell. The kinetic cell was divided in three regions: Zone 1

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RESULTS AND DISCUSSION Mesh Size and Time Step Independence. A study of mesh size independence was carried out when the coke concentration was significant in the kinetic cell and the temperature was high enough to guarantee coke combustion. These conditions were selected because they allowed us to check the response of the model to mesh size when coke oxidation, arguably the phenomenon that produces the steepest gradients in the kinetic cell, was taken place. Therefore, mesh size independence was evaluated at t = 5 min using the same conditions described above and in Table 1, except for a constant temperature of 500 K and a coke volumetric fraction of 0.05. The variables selected for the study of mesh size independence were those having major changes in space: coke volumetric fraction, oxygen molar fraction, and oxidation reaction rates of asphaltenes and coke. This paper only presents the analysis of mesh size independence for the coke volumetric fraction. This variable was the most affected by the mesh size. Plots for the other variables and a complete description of the analysis of mesh size independence is available in ref 22. Figure 2a shows the variation of the coke concentration along the kinetic cell for the different meshes evaluated. The x axis begins at a length of 0.05 m because this is where oil saturation, zone 2, starts. To complete the analysis in Figure 2a, Figure 2b shows the variation of the average coke concentration in the kinetic cell for meshes with a different number of cells. Both panels a and b of Figure 2 indicate that there is little difference in the predictions obtained by a mesh with 672 and 2000 cells. Therefore, to save computational resources, all of the results presented below were obtained with a 672 cell mesh. In addition to the study of mesh size independence, a timestep-independent study was carried out. Figure 3a shows the results of the simulation in the mesh with 672 nodes with the same conditions selected for the mesh size independence analysis, using time steps of 0.1, 0.5, 1.0, and 10.0 s. The coke concentration was again selected for the time-independent study. In Figure 3a, the predictions for all time steps are basically the same. Only for a time step of 10 s, the results present deviation in comparison to other time steps.

Figure 1. Representation of a kinetic cell in the CFD simulations: (a) oil saturation in the kinetic cell (red represents a value of 0.25) and (b) discretization (dimensions adapted from ref 16). simulates the porous medium used to obtain a good distribution of the air injected into the cell. This region is free of oil and water and guarantees that air reaches the set temperature before reacting with oil and coke. Zone 2 was saturated with oil and water. Zone 3, a region free of oil and water, helps to obtain convergence because it prevents artificial flows out of the cell. All physicochemical properties and experimental conditions required for the simulation were taken from Belgrave et al.16 and are summarized in Table 1.

Table 1. Properties of the Kinetic Cell Experiment Used in the Study length (m) diameter (m) porosity initial water saturation initial oil saturation initial gas saturation pressure (kPa) initial mole fraction of maltene initial mole fraction of asphaltene permeability (mD)

0.25 0.0508 0.412 0.05 0.25 0.7 4100 0.9151 0.0849 12000 B


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Figure 2. Selection of the mesh size. Predicted variation of the coke concentration (a) along the kinetic cell with the number of nodes as parametric and (b) with the total number of nodes.

Figure 3. Selection of the time step for the CFD simulation. Predicted variation of the coke concentration (a) along the kinetic cell with time step as the parameter and (b) with time step.

Figure 3b shows the results of the average coke concentration in the computational domain for the different time results in Figure 3a. The differences in the simulation are significant when the time step is larger than 0.5 s. For that reason, a time step of 0.5 s was selected for the simulations. This time step guarantees as well that the Courant number was below 0.1. Validation of the CFD Model with Experimental Data. The research of Hayashitani et al.23 was used to evaluate the UDFs developed for the thermal cracking reactions. In ref 23, Athabasca bitumen was thermally cracked in a quartz glass tube at a constant temperature in a closed system under an inert atmosphere. The gas and oil products were monitored at different times. Three series of experiments were carried out at different temperatures, but as a result of space restrictions in this paper, we only present the comparison of the data reported at 397 °C to the CFD predictions in Figure 4. A more complete comparison of the results in ref 23 as well as the experimental data for the low-temperature oxidation (LTO) and hightemperature oxidation (HTO) processes in ISC described in refs 24 and 25 is available in ref 22. The mass percentages of the pseudo-components, particulary those of maltenes and asphaltenes in the oil phase, were captured by the CFD simulation. The predictions for gas and coke in their absolute values present some differences with the experimental data. However, the tendency was correctly reproduced, particularly taken into account the difficulties of representing a complex structure, such as oil, with the few pseudo-components that the reaction mechanism of Belgrave et al.16 considers. Clearly, the

Figure 4. Validation of the CFD model with experimental data for the cracking of Athabasca bitumen taken from ref 23: symbols, experiments; lines, model.

CFD code reproduces the behavior of the main species during ISC, although some differences in the predictions of the absolute values are evident. Analysis of the CFD Predictions of the Spatial and Temporal Variations of the Main Variables Involved in the ISC. Figure 5 shows as isocontours the results of the CFD simulation of the kinetic cell for the volumetric fraction of oil (Figure 5a) and coke (Figure 5b) and the mass fractions of oxygen (Figure 5c) and maltenes (Figure 5d) for different times. Early in the experiment (0.2 h), the temperature is low and the oil conversion is low. At an intermediate time (t = 2.0 C


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Figure 5. Predicted variation of (a) oil saturation, (b) coke volumetric fraction, (c) oxygen mass fraction, and (d) maltene fraction inside the kinetic cell with time as the parameter.

Figure 6. Predicted variation of (a) oil saturation and (b) coke volumetric fraction with Da as the parameter. The figure also shows results from the 0D model.

also detected by Belgrave et al.,16 these authors addressed the problem by dividing the simulation domain in just three cells, each of 8.3 cm, too large to capture the heterogeneity in the concentration profile along the cell that is evident in Figure 5. The implication of the non-homogeneous character of the kinetic cell when determining the kinetics for the ISC process has not been addressed, at least in the referred literature. Effect of the Cell Operational Parameters on the Concentration Gradients in the Kinetic Cell. Because homogeneity in the kinetic cell simplifies the determination of kinetic parameters given that an assumption of a 0D model for the reactor would in that case apply, it is desirable to determine operational conditions that minimize concentration gradients along the cell. A common analysis used in chemical reactors to address dispersion makes use of the dimensionless Damköhler number (Da) that correlates the rate of consumption of a

h), the temperature is enough to activate the oxidation reactions in the oil phase; these reactions consume the oxygen of the gas phase and the lighter species in the oil phase, as evident from the maltene mass fraction. At higher times (t = 4.1 h), the lighter species in the oil phase are completely consumed and coke production increases mainly as the result of the oxidation of species of high molecular mass in the oil phase. At these times, oxygen consumption is the highest and the reaction zone narrows. Closer to the end of the experiment (t = 6.0 h), all of the species in the oil phase are consumed, coke generation stops, and only coke oxidation takes place in the cell. Figure 5 makes it evident that the behavior in the kinetic cell is distant from that of a perfect mixed reactor because significant differences were found in the concentration of the pseudo-components along the cell. Althought this behavior was D


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Figure 7. Deviation, represented by δ (see eq 2), of the CFD model with a perfect mixing model for different Da numbers: (a) oil saturation and (b) coke concentration.

reactant with its rate of transport by convection. To determine the conditions at which the behavior of the kinetic cell is similar to that of a perfectly mixed reactor, we modified operational conditions, such as the length of the cell saturated with oil, the initial oil saturation, the air injection velocity, and the oxygen molar fraction of the oxidizer, to obtain different values of Da, so that it was possible to correlate Da with the magnitude of the concentration gradients in the cell. Equation 1 presents the definition of Da considered in this study Da =

τϕSoρo xO2ρg

δoil =

x |SoCFD − So0D| Somax

× 100%

(2) L Panels a and b of Figure 7 show the variation of δoil and δcoke with time, respectively, with Da as the parameter. The highest values of δ took place around 2 h when the rate of oil consumption and coke concentration were the highest. δcoke presents a second maximum around 4 h that corresponds to a narrowing in the reaction region that is evident at t = 4.1 h in Figure 5c. In panels a and b of Figure 7, for low Damköhler numbers, the deviation of the CFD simulation with the 0D model is low. This indicates that the approximation of complete mixing is reasonable and the use of a 0D model is valid for low Damköhler numbers. To further investigate the effect of Da on the concentration gradients in the cell, we conducted simulations for the cases defined in Table 2. For all of these cases, the variations of Da

(3.431xmalPO0.4246 k m + 7.513xaspPO4.7627 ka 2 2

+ 1.232PO2kc)

∫0

(1)

where τ is the residence time for oxygen in the cell calculated at inlet conditions, ϕ is the porosity, So is the initial oil saturation, ρj is the molar density of phase j, PO2 is the partial pressure of oxygen, xi is the molar fraction of species i, and kk is the kinetic constant of reaction k. In eq 1, the term in the parentheses represents the consumption of oxygen by the oxidation of maltenes, asphaltenes, and coke. The convective transport of oxygen is implicit in the residence time. Panels a and b of Figure 6 present the predicted average oil saturation and coke concentration in the kinetic cell, respectively, when the residence time and, therefore, the Da number was modified varying the length saturated with oil from 25 to 2.1 cm. The longer the length of core saturated, the higher the residence time and the oil/air ratio. Figure 6 also presents, as standard for 0D behavior, results when the system was modeled as a semi-batch reactor. The variation of the average oil saturation in the kinetic cell with time presented a significant deviation from the 0D model only for values of Da higher than 10. The difference between the 0D model and the CFD simulations at different values of Da was more evident for the average coke concentration, because only for Da lower than 5, the system behaved similar to a perfectly mixed reactor. Equation 2 defines a parameter δ that quantifies the deviation of the predictions for average oil saturation, S, between the CFD and 0D models. A similar expression was used to account for the differences in the predictions of the other variables by both models. In eq 2, L represents the length of the bed saturated with oil and Somax represents the maximum value of saturation.

Table 2. Cases Used in the Analysis of the Homogeneity in the Cell case

So

xO2

oxidant flow (standard m3/h)

base case case 2 case 3 case 4

0.25 0.25 0.15 0.25

0.21 0.21 0.21 0.30

0.081 0.198 0.081 0.081

were obtained by changing the length of the cell saturated with oil, as described above; however, changes in operational parameters, such as oxidant flow, initial oil saturation, and oxygen molar fraction, allowed for the exploration of a wider range of Da values. With an analysis carried out similar to the analysis described above for the base case, plots with the same characteristics as those of Figure 7 were prepared for all of the other three cases and are available in ref 22. To make the results more evident in one plot, the area under the curve δSo or δcoke versus time, i.e., the curves in Figure 7, was computed for the four cases and plotted againts Da in Figure 8. In Figure 8a, it is evident that Δoil, the area under the curve in Figure 7, increases with the increase in Da. Furthermore, operational conditions that ensure Damköhler numbers lower than 11 guarantee values of Δoil below 10%, a value that suggests low concentration gradients in the cell. In Figure 8b, Δcoke presents a behavior similar to that of Δoil because its value E


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Figure 8. Variation of Δi, the area under the curve in Figure 7, with Da for (a) oil saturation and (b) coke concentration.

Figure 9. Variation of the parameter Δ for (a) oil saturation and (b) coke concentration with λ.

increased as Da became higher. A value of Da < 7 was required to guarantee Δcoke < 10% While Da, as Figure 8 showed, is a good parameter to understand the extent of homogeneity in the cell, the ISC literature1 often uses parameters that, for a constant temperature and pressure, had a nature similar to that of Da. One of these parameters that we will refer to as λ because of its distant analogy to the λ number in the combustion literature is defined in eq 3. λ=

initial oil load oxygen flux

⎛ kg ⎞ ⎜ 3 2 ⎟ ⎝ m /m s ⎠

gradients in a kinetic cell, per se, is not a drawback of the experiment unless, as is often the case, the data from the kinetic cell is used to determine kinetic parameters using a 0D model that inherently assumes a homogeneous concentration throughout the cell. This assumption that is commonly used during the analysis of experimental data obtained in a kinetic cell could have a significant impact on the kinetic mechanism if the behavior in the kinetic cell is far from that found in a perfectly mixed reactor. To address the magnitude of this impact, kinetic parameters were calculated on the basis of the results obtained in each CFD simulation carried out to obtained the data in Figures 6−9. A multi-function optimization was performed, with the function “fmincon” of MATLAB to compute the kinetic parameters involved in the oxidation reactions that best adjusted to the data obtained in the CFD to the 0D model described above. The kinetic parameters of the pyrolysis reactions were not adjusted and were maintained as those proposed by Belgrave et al.16 because they do not depend upon the oxygen concentration, the species responsible for the concentration gradients in the cell. The cost function considered the difference between CFD simulation results taken as a surrogate for experimental data and the predictions of the 0D model. The optimization only considered the pre-exponential factors because all of the activation energy was maintained constant and equal to that reported in the research of Belgrave et al.16 Furthemore, because the reactions for maltene and asphaltene oxidation were found to be highly coupled, the optimization only considered the pre-exponential factor for the reaction of coke formation. While, because of these assumptions, this

(3)

Figure 9 shows the variation of Δoil and Δcoke with λ. Although the trend of the variation of Δ with λ in Figure 9 follows the same trend observed for the variation of Δ with Da, the slope of the Δ versus Da curve is higher than that of Δ versus λ, which suggests that Da is a better metric for homogeneity because it would more readly reveal the existence of concentration gradients in the cell. Notwithstanding this, λ is a good alternative to Da because it also indicates, although to a lower extent, how homegeneous the concentration is in the combustion cell. Probably the main advantage of λ is that it involves a simpler calculation than that of Da. Implications of the Existence of Concentration Gradients on the Analysis of Experimental Data from a Kinetic Cell. The application of ISC to reservoirs would, undoubtedly, involve significant concentration gradients in the field. Successful analysis of ISC in a combustion tube depends upon the formation of the temperature and concentration gradients along the tube length. Therefore, the existence of F


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experiments are conducted at higher values of Da, the kinetic values can be significantly underestimated by even more than 1 order of magnitude.

optimization procedure can only be considered as approximate, it gives an idea of the error associated with modeling kinetic cells that are not homogeneous using a perfectly mixed reactor model. All of the data point series in a concentration−time plot (such as in Figure 5) were input to the optimization routine. All of the CFD cases analyzed guaranteed complete oil consumption, although the time required for conversion varied from simulation to simulation. To quantify the error associated with the estimation of kinetic parameters using a 0D model when concentration gradients are present, we defined δk in eq 4 as the ratio between the pre-exponential factor obtained from an optimization of the exit concentration in CFD simulations at different values of Da [(k)Da] and a theorical value that was taken as that reported by ref 16 [(k)theory]. Because a set of kinetic parameters should have as little as possible dependence upon the experimental conditions, so that the results obtained in a kinetic cell could be extrapolated to the reservoir simulation, one would expect that, for the different values of Da, δk should be close to 1. However, Figure 10 shows that, as

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*Telephone: 00-57-4-4255317. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Major financial support for this research was provided by the Colombian Administrative Department of Science, Technology and Innovation (Departamento Administrativo de Ciencia, Tecnologá e Innovación Colciencias) and ECOPETROL under Contract RC 0264-2013. Sebastian López thanks Colciencias for partil support under Program “Jovenes Investigadores e Innovadores 2011”.

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Da increases, δk is higher. This indicates that the effect of concentration gradients in the cell can impact the evaluation of kinetic parameters. The extent of this effect would be related to the value of Da.

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(k)Da (k)theory

REFERENCES

(1) Sarathi, P. S. In Situ Combustion HandbookPrinciples and Practice; National Petroleum Technology Office, Tulsa, OK, 1999; DOE/PC/91008-0374, DOI: 10.2172/3175. (2) Drici, O.; Vossoughi, S. JPT, J. Pet. Technol. 1985, 37, 731−735. (3) Kök, M. V. J. Therm. Anal. Calorim. 2009, 97, 397−401. (4) Bagci, S. Energy Sources 2005, 27, 579−588. (5) Kök, M. V. J. Therm. Anal. Calorim. 2006, 84, 361−366. (6) Couch, E. J.; Rodriguez, H. V. Effects of porosity combustion and permeability on in-situ combustion fuel consumption. Proceedings of the SPE Production Techniques Symposium; Wichita Falls, TX, May 14− 15, 1970; DOI: 10.2118/2873-MS. (7) Gates, C. F.; Ramey, H. J., Jr. JPT, J. Pet. Technol. 1980, 32, 285− 294. (8) Alamatsaz, A. R.; Moore, R. G.; Mehta, S. A.; Ursenbach, M. G. J. Can. Pet. Technol. 2011, 50, 48−67. (9) Alamatsaz, A.; Moore, R. G.; Mehta, S. A.; Ursenbach, M. G. A new understanding of an old EOR concept for in situ combustion processes. Proceedings of the SPE Western Regional Meeting; Bakersfield, CA, March 21−23, 2012; DOI: 10.2118/154723-MS. (10) Bazargan, M.; Chen, B.; Cinar, M.; Glatz, G.; Lapene, A.; Zhu, Z.; Castanier, L.; Gerritsen, M.; Kovscek, A. R. A combined experimental and simulation workflow to improve predictability of in situ combustion. Proceedings of the SPE Western Regional Meeting; Anchorage, AK, May 7−11, 2011; DOI: 10.2118/144599-MS. (11) Kovscek, A. R. J. Pet. Sci. Eng. 2012, 98−99, 130−143. (12) Kristensen, M. R.; Gerritsen, M. G.; Thomsen, P. G.; Michelsen, M. L.; Stenby, E. H. Efficient reaction integration for in-situ combustion simulation. Transp. Porous Media 2006, 1−36. (13) Ursenbach, M. G.; Moore, R. G.; Mehta, S. A. J. Can. Pet. Technol. 2010, 49, 48−54. (14) Glatz, G.; Hascakir, B.; Castanier, L.; Clemens, T.; Kovscek, A. R. Kinetic cell and combustion tube results for a Central European crude oil. Proceedings of the SPE Annual Technical Conference and Exhibition; Denver, CO, Oct 30−Nov 2, 2011; pp 1−27, DOI: 10.2118/146089-MS. (15) Moore, R. G.; Laureshen, C. J.; Ursenbach, M. G.; Mehta, S. A.; Belgrave, J. D. M. SPE Reservoir Eval. Eng. 1999, 2, 565−571. (16) Belgrave, J. D. M.; Moore, R. G.; Ursenbach, M. G.; Bennion, D. W. SPE Adv. Technol. Ser. 1993, 1, 98−107. (17) Lapene, A.; Debenest, G.; Quintard, M.; Castanier, L. M.; Gerritsen, M. G.; Kovscek, A. R. Energy Fuels 2011, 25, 4886−4895. (18) Gerritsen, M. G.; Kovscek, T. Experimental Investigation and High Resolution Simulation of In-Situ Combustion Processes; Stanford University: Stanford, CA, 2008; FC26-03NT15405, DOI: 10.2172/ 946139. (19) Coats, K. SPEJ, Soc. Pet. Eng. J. 1980, 20, 533−554.

Figure 10. Deviation in the coke oxidation parameters with the Da number.

δk =

AUTHOR INFORMATION

Corresponding Author

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CONCLUSION The development of several UDFs that address phenomena that are not readly available in commercial CFD software, such as two-phase equilibrium, saturation properties, temperature dependency of physicochemical properties, and kinetic expressions, makes it possible to model ISC experiments with CFD. The CFD simulations showed the existence of concentration gradients in kinetic cell experiments used to characterize the ISC process that indicates a behavior in the cells very distant from that of a perfectly mixed reactor. However, the analysis of experimental systems to characterize ISC with dimensionless numbers, such as the Damköhler number, can significantly help in their design, so that the analysis of the experimental results through perfectly mixed models is possible. For the experiment considered in this research, Da < 7 would guarantee that a 0D model can capture the ISC behavior with an error lower than 10%. If the G


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Criteria To Select Operational Variables That Improve the Accuracy of

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