Isoconversional Kinetic Analysis of the Combustion of Heavy

Energy & Fuels 2009, 23, 4003–4015

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Isoconversional Kinetic Analysis of the Combustion of Heavy Hydrocarbons Murat Cinar, Louis M. Castanier, and Anthony R. Kovscek* Energy Resources Engineering, Stanford UniVersity, Stanford, California 94305 ReceiVed March 13, 2009. ReVised Manuscript ReceiVed June 4, 2009

One method to access unconventional, heavy-oil resources as well as waterflood residual oil is to apply in situ combustion (ISC) to oxidize in place a small fraction of the hydrocarbon, thereby providing heat to reduce oil viscosity and pressure that enhances recovery. Experimental analysis of crude-oil oxidation kinetics provides parameters, such as activation energy, for modeling and optimization of ISC processes. The complex nature of petroleum as a multicomponent mixture and multistep character of oxidation reactions substantially complicates the kinetic analysis of crude-oil oxidation. An isoconversional technique is reported to provide a model-free method for estimating activation energy. The technique naturally deconvolves multistep reactions, providing a useful diagnostic tool that characterizes the combustion qualities of different oils. The experimentally determined combustion kinetics of three crude oil samples, including Hamaca (Venezuela), are explored, adding to the knowledge base of crude-oil combustion. All samples exhibit fairly constant apparent activation energies of about 50 000 J/mol for so-called high-temperature oxidation reactions that occur in the range of 625-700 K. The so-called low-temperature oxidation reactions that occur in the vicinity of 500 K display significant variability and are difficult to group and characterize with a single activation energy. Synthetic examples augment the experimental program and document the diagnostic characteristics of the isoconversional technique applied to crude oil, thereby providing insight into the burning qualities of oil. Phenomena, such as “cool flames”, are identified and marked by negative apparent activiation energy.

1. Introduction In situ combustion (ISC) is an effective thermal-enhanced oil recovery process that provides an important alternative to steam injection. Although technically effective, it is not applied widely. The ISC process is somewhat difficult to engineer and monitor because of a lack of predictive tools. In contrast, the most widely used thermal recovery method is steam injection. Steam injection, however, is not applicable to all reservoirs. The depth of the reservoir and the pressure conditions constitute two major constraints for steam injection. In the case of deep reservoirs, heat losses from the injection well to the surrounding formation cause steam to condense and make steam injection both difficult and inefficient. Additionally, as pressure increases, the latent heat of water decreases, resulting in a greater fraction of the energy of the injectant being carried as sensible heat. Clearly, steam injection is limited by the critical pressure of water. Despite its usefulness, steam injection is limited to a select group of reservoirs. On the other hand, ISC is not nearly as limited. Two possible scenarios where ISC could be feasible and steam injection much more difficult to implement are offshore fields and reservoirs lying under permafrost. Because of reduced heat losses and the containment of combustion products within the reservoir, ISC is more energyefficient and involves fewer atmospheric emissions than steam. Additional benefits of combustion are the in situ upgrading of heavy oils because the heaviest fraction of the crude oil is consumed during the process and also reduction in sulfur content as a result of the combustion process.1 ISC includes aspects of different recovery techniques, such as CO2 flooding and steam * To whom correspondence should be addressed. E-mail: kovscek@ stanford.edu.

flooding. As a result, modeling of complex ISC processes requires an understanding of the behavior of different physical phenomena, such as phase change, chemical reactivity, as well as heat and mass transfer. In this study, the focus is the kinetics of ISC, their improved measurement, and accurate representation of crude-oil reactivity. Improved analysis of combustion kinetics is a first step in developing predictability of ISC at the laboratory and field scale. Crude oil is a complex material formed by hundreds of hydrocarbon components. To model the reactions that occur in a combustion process, an extended compositional analysis and a large number of kinetic expressions are required. It is not easy, however, to describe all of the reactions associated with the oxidation of all components. Only for the simplest hydrocarbon molecules (e.g., CH4) are detailed models available. In addition, how individual mechanisms combine is still a question. Even if such multistep, elementary reaction models were available, it is difficult to implement them in numerical reservoir simulators. Elementary reaction models require many computational steps, and it is likely that excessive computational time is needed when reaction and flow are coupled. Instead, simple models based on the pseudo-component assumption appear in the literature.2-5 In those models, crude oil is assumed to be a single component and the reactions are grouped together. Reactions during combustion of oil in porous media are generally grouped into three functional groups: low-temperature oxidation (LTO), fuel deposition (MTR), and fuel combustion (HTO).4 (1) Castanier, L. M.; Brigham, W. E. Upgrading of crude oil via in-situ combustion. J. Pet. Sci. Eng. 2003, 39, 125–136. (2) Bousaid, I. S.; Ramey, H. J., Jr. Oxidation of crude oil in porous media. Soc. Pet. Eng. J. 1968, 137–148. (3) Burger, J. G.; Sahuquet, B. Chemical aspects of in-situ combustionsHeat of combustion and kinetics. Soc. Pet. Eng. J. 1972, 410–422.

10.1021/ef900222w CCC: $40.75  2009 American Chemical Society Published on Web 07/06/2009

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LTO reactions yield water and partially oxygenated compounds. Their characteristic is the negative temperature gradient region, over which the oxygen reaction rate decreases as the temperature increases.6 MTR reactions are basically fuelformation reactions. The HTO reactions are heterogeneous and include carbon bond reactions of oxygen with fuel producing carbon oxides and water. Kinetic analysis of crude oil reveals kinetic parameters, such as the activation energy and the preexponential factor associated with these reaction groups. One experimental technique to estimate kinetic parameters is to use ramped temperature oxidation (RTO) with effluent gas analysis as described by Fassihi.4 In addition, there are other conventional tools, such as accelerated rate calorimetry (ARC)5 and thermogravimetric analysis (TGA).5,7 Their differences aside, these methods merge in their assumptions regarding the reaction model. Similar to other conventional kinetic analyses, these techniques assume a reaction model to interpret the experimental data.8 Typically, only single, lumped LTO and HTO reactions are considered. Lumping components, grouping reactions, and assuming reaction models may develop an oversimplified picture of crude-oil combustion. Alternatively, isoconversional methods provide a model-free technique to estimate activation energy. Cinar et al.9 applied isoconversional methods to the analysis of RTO kinetic data and reported great potential. Multistep reactions were naturally deconvolved, thereby avoiding any uncertainties associated with the assumption of a reaction model. Isoconversional methods are also useful as a diagnostic tool to recognize the burning characteristics of different oils.9 In this study, the isoconversional technique is applied to RTO experiments of crude oil with effluent gas analysis and the technique is validated. First, the applicability of the isoconversional method to multistep oxidation of oil in porous media is established via synthetic examples, and different isoconversional methods are compared. Then, a synthetic example illustrates the technique in practice and explores its limits. Finally, the diagnostic properties of the isoconversional method are examined by considering three different oil samples and a synthetic example.

absolute temperature (K), R is the gas constant (J mol-1 K-1), and A is a pre-exponential factor sometimes referred to as the Arrhenius constant. Similar forms are applied by various authors.2-4 Beyond its wide application, eq 1 is the simplest form of a combustion rate equation. In reality, oxidation of hydrocarbons involves chain reactions with degenerate branching,10 probably leading to a complicated reaction scheme with an overall reaction expression that may not be entirely represented by eq 1. The isoconversional method provides a way to bypass the complex, unknown reaction models. Numerous experiments at different heating rates are performed to probe and parametrize the reaction. In a more general expression, the reaction rate is written as a product of the rate constant that is a function of the temperature and reaction model that is a function of the concentration. Representing the reaction model with f(C), we have -

dC ) k(T)f(C) dt

where k(T) is the rate constant (units depend upon the reaction model) and f(C) is the reaction model. The rate constant is expressed as a function of the temperature. Assuming Arrhenius behavior, we have dC ) Ae-E/RTf(C) dt

dX ) Ae-E/RTf(X) dt

dCf ) Ae-E/RTPOa 2Cfb dt

(1)

( dXdt ) ) ln(A) + ln[f(X)] - RTE

(5)

At constant values of conversion, f(X) is assumed to be constant. This is analogous to assuming that the chemistry of the process is independent of the temperature and only dependent upon the level of conversion.11 Thus, the reaction model is independent of the heating rate. As a consequence, for different temperatures at the same conversion levels or isoconversional values, f(X) is equal. Then

where b and a represent exponents for carbon and oxygen partial pressure, respectively, E is the activation energy (J/mol), T is (4) Fassihi, M. R. Analysis of fuel oxidation in in-situ combustion oil recovery. Ph.D. dissertation, Stanford University, Stanford, CA, April 1981. (5) Sarathi, P. In-Situ Combustion HandbooksPrinciples and Practices; National Petroleum Technology Office: Tulsa, OK, 1999; Report DOE/ PC/91008-0374, OSTI_ID 3174. (6) Moore, R. G. New strategies for in-situ combustion. J. Can. Pet. Technol. 1993, 32, 11–13. (7) Ambalea, A. M.; Freitag, N. Thermogravimetric studies on pyrolysis and combustion behavior of a heavy oil and its asphaltenes. Energy Fuels 2006, 20, 560–565. (8) Burnham, A. K.; Dinh, L. N. A comparison of isoconversional and model-fitting approaches to kinetic parameter estimation and application predictions. J. Therm. Anal. Calorim. 2007, 89, 479–490. (9) Cinar, M.; Castanier, L. M.; Kovscek, A. R. Improved analysis of the kinetics of crude-oil in-situ combustion. In SPE Western Regional Meeting 2008, Bakersfield, CA, March 31-April 2, 2008; SPE Paper 113948.

(4)

The isoconversional principle states that, at a constant extent of conversion, the reaction rate is only a function of the temperature. Equation 4 is the basis of all isoconversional methods discussed in this work. Taking the logarithm of eq 4 gives

2. Isoconversional Approach

-

(3)

In terms of fractional conversion, X, eq 3 is represented as

ln ISC reaction rates are commonly described as a function of the fuel concentration and oxygen partial pressure.2 Assuming Arrhenius behavior for the rate constant, this model is

(2)

EX RTX

(6)

m ) ln(A) + ln[f(X)]

(7)

ln

( dXdt )

X

)m-

where

Here, TX is the temperature for any particular experiment at conversion X. The symbol EX is the activation energy at conversion X. For different temperatures, we plot the left-hand side (LHS) of eq 6 with respect to -1/TX. The slope of the graph gives EX/R, and the intercept is m. This method was first (10) Semenov, N. Chemical Kinetics and Chain Reactions; Oxford University Press: London, U.K., 1935. (11) Friedman, H. L. Kinetics of thermal degradation. J. Polym. Sci., Part C: Polym. Lett. 1964, 6, 183–195.

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introduced by Friedman11 and is referred to in the literature as the method of Friedman or the differential isoconversional method. This method needs reaction rate values to be obtained, and the rate values are usually calculated by numerical differentiation. It is well-known that numerical differentiation amplifies error in experimental data. Therefore, results are sensitive to experimental noise.12 To avoid numerical differentiation, integral isoconversional methods are developed. A linear ramped temperature heating rate is expressed as T ) T0 + βt

(8)

Here, β is the heating rate (T/time), and T0 is the base temperature (T). By combining eq 8 with eq 4 and with some algebraic manipulation, we have ln(β)X ) ln

∫

∞ -2

x

x

[ AER g(X)]

exp(-x)dx - ln

(9)

where x)

E RT

(10)

ln(β)X = -1.052

∫

g(X) )

∫

X

0

dX f(X)

(11)

The integral on the right of eq 9 has no general analytical solution. For hyperbolic and parabolic heating programs, this integral has analytical solutions. The integral isoconversional methods differ in their approximation to the solution of this integral, as described next. The Kissenger, Akahira, Sunose (KAS)13,14 method uses the approximation

∫

∞ -2

x

x

exp(-x)dx ≈ x-2 exp(-x)

(12)

The approximation is assumed to be valid for values of x between 20 and 50. Substituting eq 12 in eq 9, we have β T

()

ln

=X

( ) [

R E 1 g(X) - ln R TX AE

]

(13)

The Ozawa-Flynn-Wall (OFW)15,16 method uses another approximation

∫

∞ -2 x x

exp(-x)dx ≈ exp(-1.052x - 5.33)

[

]

X

0

dX )A f(X)

∫

tX -E/RT(t ) X

e

0

dt

(12) Vyazovkin, S. Evaluation of activation energy of thermally simulated solid-state reactions under arbitrary variation of temperature. J. Comput. Chem. 1997, 18, 393–402. (13) Kissinger, H. E. Reaction kinetics in differential thermal analysis. Anal. Chem. 1957, 29, 1702–1706. (14) Akahira, T.; Sunose, T. Research Report. Chiba Institute of Technology, Narashino, Chiba, Japan, 1971; Vol. 16, p 22. (15) Ozawa, T. A new method of analyzing thermogravimetric data. Bull. Chem. Soc. Jpn. 1965, 38, 1881. (16) Flynn, J. H.; Wall, L. A. A quick direct method for the determination of activation energy from thermogravimetric data. Polym. Lett. 1966, 4, 323.

(16)

and

∫

tR -E /RT R R

J[E, T(t)] )

0

e

dt

(17)

The reaction model is taken as independent of the temperature for a given conversion and experiments conducted with different heating histories. One can then write AXJ[EX, T1(tX)] ) AXJ[EX, T2(tX)] ) ... ) AXJ[EX, Tn(tX)] (18) AX values cancel in eq 18. The objective function to be minimized is the double sum of the ratio of J evaluated at equal conversion with temperatures Ti and Tj and differing times from the various experiments12 Φ(EX) )

n

n

i

j

J[EX, Ti(tX)]

∑ ∑ J[E , T (t )] ) min X

i*j

(19)

j X

The expected value of eq 19 is expected value [Φ(EX)] )

n! 2n! ) 2!(n - 2)! (n - 2)!

(14)

This approximation is assumed to be valid for values of x between 20 and 60. Substituting eq 14 in eq 9, we have

(15)

The procedure to estimate activation energy from the above methods requires that a series of experiments be conducted with different heating rates. The major disadvantage of these integral methods is their approximations. Because these methods were derived assuming contant activation energy, resulting errors should be dependent upon the variation of activation energy with conversion.8 The heating program of the experiments is prescribed to control the experiment. Note that the KAS and OFW methods require linear heating given by eq 8. By the virtue of thermal effects of reactions (endothermic or exothermic behavior), the temperature of the system deviates from the prescribed heating program. A computational method that accounts for any variation of temperature is proposed by Vyazovkin.12 As shown by Vyazovkin,12 these deviations of temperature yield erroneous values of activation energy, when such a data set is used with a model that assumes linear heating. Also, all integral isoconversional techniques have internal errors related to the approximation assumed. To overcome those issues, a nonlinear isoconversional method is proposed by Vyazovkin.12 Integrating eq 4,

and g(X) )

( )

R E 1 g(X) - 5.33 - ln R TX AE

(20) and the number of combinations is (n / 2), where n is the number of experiments. In theory, a reaction occurs at any temperature greater than absolute zero. Then, we reorganize the integral given by eq 17 here J[E, T(t)] ) J0 + J0 )

∫

∫

tX -E/RT(t ) X

t0

e

dt

t0 -E/RT(t)

0

e

dt

(21) (22)

While time goes from 0 to t0, temperature goes from absolute zero to T0. Define a quasi-linear (β*) heating rate that is the

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Figure 1. Experimental apparatus for ramped temperature oxidation experiments.

slope of temperature against time t0 )

T0 β*

(23)

While taking experimental measurements, we assume that the starting time is 0. Then, we add t0 to our time measurements, and J0 is calculated by the approximation given by Senum and Yang.17 J0 ≈ (β*)-1

(x2 + 10x + 18) E exp(-x) 3 R x (x + 12x2 + 36x + 24)

(24)

Details of implementation follow. Required isoconversional values of temperature and time are estimated by polynomial interpolation.18 To minimize eq 19, the Brent algorithm18 is used. This algorithm requires that a bracketing triplet of abscissas Φ1, Φ2, and Φ3, such that Φ2 is between Φ1 and Φ3 and Φ2(E2) is less than both Φ1(E1) and Φ3(E3), is given as input. We choose E2 )

E1 + E3 2

(25)

We can further improve our initial guess (E2) by assuming that Φ(EX) (eq 19) is approximated by a quadratic parabola Φ(EX) ) rE2X + sEX + t

(26)

Then, the minimum of a quadratic parabola is equal to E0 ) -

s 2r

(27)

As an aside -

E23(Φ1 - Φ2) + E21(Φ2 - Φ3) + E22(Φ3 - Φ1) s )2r 2[E3(Φ2 - Φ1) + E2(Φ1 - Φ3) + E1(Φ3 - Φ2)] (28)

E1 and E3 are chosen as user input. Generally, the algorithm

converges quickly regardless of the choices for E1 and E3. Simpson’s rule is used to calculate integrals.18 The above procedures assume constant activation energies. If the process involves a variation of activation energy with respect to conversion, the estimated activation energies become averaged over the region 0-X. In addition, the resulting activation energies undergo smoothing over the region.19 The amount of error introduced depends upon the application and the associated reaction scheme. To overcome this issue, an isoconversional method that accounts for variation in the activation energy is proposed by Vyazovkin.19 By modifying eq 17 as given below, the resulting activation energies are averaged over the small interval ∆X J[E, T(t)] )

∫

tX

tX-∆X

e-E/RT(tX)dt

(29)

3. Experimental Apparatus and Procedures In this study, RTO experiments with analysis of the effluent gas are conducted. Previous studies at Stanford have produced an experimental apparatus for both RTO and combustion experiments.4,20 On the basis of this apparatus, a new system was designed and built, as shown in Figure 1. Also, the main components of the system are given by Table 1. The system is designed to operate and acquire data automatically without any user action during an experiment. The system is equipped with a temperature-limit controller and relief valves in the case of any failure of the temperature controller and back-pressure regulator, respectively. The system includes a tubular reactor, also referred to as a kinetics cell. Appropriate filters and liquid traps are placed to prevent any contamination in the system, especially in the gas analyzer. (17) Senum, G.; Yang, R. T. J. Rational approximations of the integral of the Arrhenius function. Therm. Anal. 1979, 11, 445. (18) Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; Vetterling, W. T. Numerical Recipes in C: The Art of Scientific Computing; Cambridge University Press: Cambridge, U.K., 1986; p 329. (19) Vyazovkin, S. Modification of the isoconversional method to account for variation in the activation energy. J. Comput. Chem. 2001, 22, 178–183. (20) Mamora, D. D. Kinetics of in-situ combustion. Ph.D. dissertation, Stanford University, Stanford, CA, May 1993.



Table 1. Experimental Equipment mass flow controller gas flow meter gas analyzer temperature controller data logger digital thermometer back-pressure regulator temperature-limit controller relief valves furnace

Brooks Instruments, model 5850E Omega, model FMA-1600A Servomex Xentra analyzer, model 4200C Omega, model CN 8201 Measurement Computing, model USB-TC Omega, model 2176A Swagelok, KFB series Omega, CN3261 Swagelok, R3A series Marshall, model 1046

A typical experiment starts with preparation of the sample. The sample is a mixture of sand (or crushed reservoir rock), water, and an appropriate amount of oil. The mass of oil used should be determined by a trial and error procedure. The amount of oil should be small enough to minimize temperature deviations from the preprogrammed temperature history and large enough to produce sufficient effluent gas for analysis. Then, the sample is packed into the kinetics cell, and the cell is placed in the furnace. Several thermocouples are used to measure temperature at various points in the cell and in the furnace to check for uniformity of temperature. Temperature in the cell is measured at three different locations along the axis (bottom, top, and center) to make sure that the temperature in the cell varies by at most 1-2 °C such that the assumption of perfect mixing holds. Because the measured temperatures in the cell are very close to each other, no sensible combustion front is developed. Clearly, the reactor operates in a differential fashion. For calculations, with the temperature in the center of the reactor, indeed, there is no significant difference in results using the temperature from any of the thermocouples. Air is passed through the cell while increasing the temperature linearly. The pressure at the inlet and outlet of the cell, exit flow rate, temperature in the cell and furnace, and effluent gas composition (CO2, CO, CH4, and O2) are recorded continuously during the experiment. The isoconversional technique requires a series of experiments to be conducted at different heating rates. All of the other parameters, such as pressure, flow rate, initial temperature, etc., are held fixed for all tests. Therefore, each experiment is conducted with great care to achieve satisfactory and consistent results with the proposed analysis technique. For this reason, preparation of the test sample has great importance. There are two approaches: either prepare a single sample for each run or prepare a large enough sample for at least 10 separate runs. The second approach guarantees that the same sample is used for each run. This larger sample, however, needs to be kept in an oxygen-free environment (for example, stored under N2) to avoid any oxidation reactions prior to testing. Previous trials without storage under an inert atmosphere showed deviations in temperature histories and inconsistencies in reaction rates. It is our experience, nevertheless, that preparation of a large sample does not guarantee consistent results among the various tests at different heating rates even if the sample is kept under an inert environment, such as nitrogen. It is advised to prepare a single sample just before each experiment with immense care. The proportions used are 4 g of water and 42 g of solid and oil (sample size differs by 4-2 g). The solid material is either crushed reservoir material or 60 mesh sand. Clay, such as kaolinite, is known to affect reaction kinetics positively4 and is a natural component of siliceous reservoirs. As noted below, 4 g of clay is added during some tests that employ sand. 3.1. Design Equations for Kinetic Runs. In this section, the design equations for the reactor are given and the assumptions regarding the analysis are justified. The equations also form the basis of a synthetic example. We start with a mole balance for each component. First, consider that fuel is only consumed because there is no in or out flow of fuel. Fuel is defined as the immobile portion of the oil that contributes to reactions. Because oil distills during the experiment, condensates are produced but do not contribute to reactions. The mole balance yields

rf ) -

dCf dt

(30)

Now consider air. Air is injected and is in excess throughout the cell during the experiment. Upon assumption of perfect mixing and that fuel is consumed over the total volume

FO2,0 - FO2 V

+ rO2 )

dCO2 dt

(31)

The accumulation term is negligible in view of the large air injection rate, small total volume, and the molar concentration of fuel that is much larger than the molar concentration of oxygen at a given time

FO2,0 - FO2

-rO2 )

V

(32)

The rates of disappearance of fuel and oxygen are related through stoichiometric coefficients. Define R as the number of moles of oxygen consumed per mole of fuel that reacts

rO2

rf )

(33)

R

In the experiments, effluent gas analysis is used. Therefore, the oxygen consumed is measured rather than the weight of the fuel. Using eqs 32 and 33, oxygen consumption is related to the rate of disappearance of fuel, avoiding any discrepancies introduced by phase change. The rate of disappearance of fuel takes the following form

-

FO2,0 - FO2 1 dCf ) dt V R

(34)

If we integrate eq 34 and rearrange in terms of conversion, we obtain

Xf(t) )

∫ (F

1 1 Cf0 RV

t

O2,0

0

- FO2)dt

(35)

It is not possible to estimate molecular weight and, accordingly, the initial concentration of fuel without an extensive compositional analysis, but it is known that, as time goes to infinity, conversion goes to unity and all fuel is consumed. Thus

1 1 ) Cf0 RV

1

∫

∞

0

(FO2,0 - FO2)dt

(36)

Then, conversion is represented as

∫ (F ∫ (F t

Xf(t) )

0 ∞

O2,0

- FO2)dt

0

O2,0

- FO2)dt

(37)

Conversion of the fuel is estimated using eq 37, and along with the temperature measurements, the isoconversional analysis is applied.

4. Synthetic Examples We first illustrate the application of the isoconversional method to crude oil using synthetic data. Oxygen consumption data is used in exactly the same fashion as analysis of the experimental results. 4.1. Example 1. Elsewhere,9 we showed via a synthetic example that the isoconversional approach was capable of

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Table 2. Arrhenius Parameters Used in the Synthetic Example Arrhenius constant activation energy (J/mol) heat of reaction (J/mol)

reaction 1

reaction 2

reaction 3

reaction 4

1 L mol-1 s-1 63000 -70000

2.93 × 105 s-1 75000 40000

100 L mol-1 s-1 125000 -140000

100 L mol-1 s-1 120000 -60000

recovering the intrinsic activation energies of a two-step, irreversible reaction. The technique appears to be particularly well-suited for this application. The intent of this section is to explore the limitations and diagnostic capabilities of the approach. Here, a more detailed model is considered along with heat released and different isoconversional methods are compared. The reaction scheme is given by eq 38. Here, the first reaction may be considered as LTO, the second may be considered as pyrolysis, and the third and fourth together may be considered as HTO reactions. This is a similar case to our experiments, where only air is injected and combustion gases along with water are produced. k1

(1) A + B 98 C k3

(2) C 98 D + F

n

˙ - FB0 Q

∑ Θ C (T - T i)1

i pi

q

i,in)

+

∑ ∆H

Rx,i,j(T)(ri,jV)

j)1

n

V

∑CC i)1

(38)

k4

k5

(4) D + B 98 H + G + F The experimental setup is simulated with the assumption of a continuously stirred tank reactor (CSTR) because concentrations of the species change little over the volume. The following set of differential equations is a direct result of mole balances for the different species. dCA ) r1,A + r4,A dt FB0 - FB dCB ) + r1,B + r3,B + r5,B dt V dCC ) -r1,C + r3,C dt dCD ) r5,D - r3,D dt FF dCF ) - - r3,F - r4,F dt V FG dCG ) - r3,G - r4,G dt V FH dCH ) - r3,G - r4,G dt V

(39)

In our kinetic runs, the temperature deviates from the preprogrammed history as a result of the exothermic reactions during combustion. To mimic this behavior, the energy balance is solved. The energy balance for the system described is Table 3. Other Parameters Used in the Synthetic Example A

B

C

200.0

35.0

100.0

D 100.0 298.15 15000 0.00004 100.0 2.0

F

G

H

50.0

60.0

35.0

,

Θi )

i pi

Fi FB0

(40)

Note that the second sum in the nominator is not a double sum. The heat of reaction i must be referenced to the same species in the rate, ri,j, by which ∆HRx,i,j is multiplied.21 The rate of heat flow into the system is represented by the following equation: ˙ ) Ua(T - Ta) Q

(3) A + B 98 H + G + F

Cp (J/mol) initial T (K) Ua (J m-3 s-1 K-1) V (m3) P (psia) q (L/min)

dT ) dt

(41)

Here, Ta is the ambient temperature, and in our case, ambient temperature is increased linearly with time given by eq 8. Ua is the overall heat-transfer coefficient multiplied by the heatexchange area. The Arrhenius relationship describes the rate constants. The parameters assumed are given in Tables 2 and 3. Note that the parameters are arbitrarily chosen within acceptable orders of magnitude. Also, normally distributed random errors are added to the synthetic data obtained. J-type thermocouples are used in the experiments. The accuracy (assumed 3σ) of those thermocouples is the greatest of 0.75% or 2.2 °C. Also, the accuracy of the gas analyzer used is 0.15% for the oxygen measurements. On the basis of these error ranges, noise is added to the data. The set of equations (eqs 39 and 40) with the list of parameters and initial values are solved with the Rosenbork method.17 The concentration profiles for B and temperature profiles are given in Figure 2. The process is simulated at five different heating rates of 1.5, 1.75, 2, 2.5, and 3.0 K/min. Different isoconversional methods are applied to the synthetic data. We apply Vyazovkin,12,19 the KAS,13,14 the OFW,16,17 and the Friedman11 methods. For the analysis, computer programs were coded for each method in C. The results are shown in Figure 3. Results indicate that we can estimate at least two different activation energies using isoconversional methods. Therefore, we can use these methods to estimate activation energies for kinetic runs. In conclusion, in the case of multiple reactions, activation energy is represented as a function of conversion. Specifically, the OFW and KAS methods did not give any significant results especially at conversions greater than 0.5, probably because of multiple reaction mechanisms along with temperature deviations. On the other hand, Vyazovkin,12 Friedman,11 and Vyazovkin19 methods all indicate two different activation energies, one at low and one at high conversions. The results of the Friedman method fluctuates just a little bit more than the Vyazovkin methods, because of numerical differentiation; however, the gas analyzer measurements are accurate enough to use the Friedman method. Surprisingly, the (21) Fogler, H. S. Elements of Chemical Reaction Engineering, 4th ed.; Prentice Hall: Upper Saddle River, NJ, 2005.



Figure 2. Simulated data with noise. Synthetic example 1, concentration profile for component B and temperature profiles at different heating rates.

Figure 3. Activation energy dependencies evaluated for synthetic example A by different methods.

Vyazovkin12 method works quite well in this case. Elsewhere,9 we showed that this method tends to smooth the results. Also note that the estimated activation energies are 10% off. This is due to the multistep reaction mechanism and estimation of A consumption from B consumption. Also, it is not possible to distinguish between reactions 3 and 4 because these reactions have similar activation energies. 4.2. Example 2. Isoconversional methods are useful as a diagnostic tool to recognize the underlying mechanisms of complex multistep reactions. One example is cool flames, an incomplete combustion associated with the negative temperature gradient region.22 In this region, oxygen uptake as well as heat released decrease with increasing temperature.23 Unlike conventional combustion that releases large amounts of heat, cool flame combustion releases little heat and the products are, for example, relatively complex oxygenated compounds that result from partial oxidation. It is possible to identify cool flames using isoconversional analysis, as shown below. The example is based on a simplified mechanism for low-temperature alkane oxidation.24 There is a significant feature of the mechanism connected to the formation of RO2 (see Figure 4). (22) Freitag, N.; Verkoczy, B. Low-temperature oxidation of oils in terms of SARA fractions: Why simple reaction models don’t work. J. Can. Pet. Technol. 2005, 54–61. (23) Moore, R. G.; Laureshen, C. J.; Ursenbach, M. G.; Mehta, S. A.; Belgrave, J. D. M. Combustion/oxidation behavior of Athabasca Oil Sands bitumen. SPE ReserVoir EVal. Eng. 1999, 2, 565–572. (24) Pilling, M. J. Low-Temperature Combustion and Autoignition, 1st ed.; Elsevier Science: Amsterdam, The Netherlands, 1997.

Figure 4. Simplified mechanism for low-temperature alkane oxidation.

In the mechanism displayed in Figure 4, RO2 radicals lead to branching, while the termination occurs through alkyl R. At high temperatures, the equilibrium shifts and the termination reactions through R are favored over branching reactions through RO2, so that the reaction occurs more slowly. This is the cause of the negative temperature gradient (versus conversion) and cool flames.24 In our simple mechanism, we have a similar rate of reaction behavior and, as a result of this behavior, isoconversional analysis estimates negative apparent activation energies.

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Table 4. Parameters for the Synthetic Reaction Model reaction k1 k2 k3 k4 k5

pre-exponential factor (L/mol)

activation energy (J/mol)

60

8.7 × 1012 1.76 × 106 600 600

1.5 K/min 2.0 K/min 2.5 K/min 3.0 K/min

63000 184000 75000 125000 120000

activation energy (J/mol)

In this example, four types of reactions are modeled: the reversible creation of intermediate, fuel*; low-temperature oxidation product creation, LTOproduct; high-temperature oxidation (HTO) of fuel; and LTOproduct. The five reactions modeled are as follows: k1

fuel + O2 {\} fuel* k2

k3

fuel* 98 LTOproduct + H2O k4

fuel + O2 98 CO2 + CO + H2O

Table 5. Estimated HTO Activation Energies with the Conventional Method

(42)

k5

LTOproduct + O2 98 CO2 + CO + H2O The parameters for the rate constant and activation energy are given in Table 4. The reactions are assumed to occur in our experimental system with the typical experimental conditions

97022

81608

71269

51648

that are given later. Temperature deviations from the preprogrammed history are assumed to be of short duration and negligible. Therefore, no heat equation is solved. The results are based on mole balance considerations. The concentration and temperature profiles are given in Figure 5. A total of four experiments at different heating rates are simulated. The flow rate is set to 2.0 L/min. The volume of the reactor is 40 cm3. The initial temperature is 298.15 K. Four heating rates are considered: 1.5, 2.0, 2.5, and 3.0 K/min. The isoconversional analysis results in the activation energies are summarized in Figure 6. Also, as given in Figure 6, the apparent activation energy is represented as a function of the temperature. Next, we apply the method described by Fassihi4 and estimate the activation energy of HTO. The results are given in Table 5. The estimated activation energy differs significantly for different heating rates. Therefore, the activation energies estimated with this method depends upon the heating rate, and all values differ from the true value of 120 000 J/mol. Although in this example isoconversional analysis did not give the input activation energy, it indicates an important phenomenon. The mechanism used is based on the aforementioned alkane oxidation. As explained above, at relatively high temperatures, the equilibrium shifts and the termination reactions

Figure 5. Simulated data: (right) specified temperature ramp and (left) oxygen consumption as a function of the time at different heating rates of synthetic example 2.

Figure 6. Isoconversional analysis results for synthetic example 2.



Figure 7. Hamaca experimental data, oxygen consumption versus time.

Figure 8. Hamaca experimental data, temperature histories. Table 6. Experimental Conditions Hamaca air flow rate (L/min) initial pressure (psia) target temperature (K) initial temperature (K) particle size (mesh) sample size (oil) (g)

2.0 100.0 923.15 298.15 60 (average) 2.0

sample A

sample B

2.0 100.0 823.15 298.15 20-42 4.0

2.0 100.0 823.15 298.15 60-42 3.0

through R are favored over branching reactions. This shift is the reason behind cool flames. In this simple mechanism, a similar observation is made. As the temperature increases, equilibrium of the first reaction shifts to the left and intermediate destruction reactions are favored over intermediate creation reactions. This is the reason for the observed negative activation energy region. As a result of this behavior, isoconversional analysis gives negative activation energies that might be associated with cool flame phenomena. Also, the activation energy of the second reaction is the greatest of all reactions considered. On the other hand, the second reaction has the greatest pre-exponential factor. As a result, the second reaction proceeds before the other reactions, even though they have lower activation energies. The LTO reactions generally strongly depend upon the surface area, and consequently, large preexponential factors for the second reaction are appropriate. 5. Results In the experimental study, three oil samples are considered. The first is a heavy crude oil from the Hamaca portion of the

Orinoco Belt (Venezuela). This sample has been analyzed previously9 and is used to answer practical questions, such as the number of ramped temperature tests to be conducted for isoconversional analysis and the degree of repeatability of the analysis. Of the various crude oils that are analyzed in the literature, Hamaca oil is well-studied and the combustion front is shown to propagate rather well during combustion tube runs in the laboratory. Two other oil samples are examined. Throughout the paper, those samples are referred to as samples A and B. For the isoconversional analyses, the Vyazovkin method19 is used. Also, the Friedman11 method is applied. The results of these two methods are identical for the cases considered. 5.1. Hamaca. In our example, five experiments are used for the application of the analysis. For the synthetic examples with a simple mechanism and no errors in data, two experiments were enough to recover the input activation energies. It is not clear, however, how many experiments are necessary for isoconversional analysis to produce reliable results under laboratory conditions. In the first investigation, the answer for this question is sought. A total of 10 experiments were conducted at eight different heating rates. Two experiments were repeated as consistency checks. The target temperature was 948.15 K. In addition to the oil and sand quantities described above, each sample has 4.0 g of clay. The gravity of the oil is 10.5° API. The experimental conditions are given in Table 6. The differences between inlet and outlet flow rates were negligible in all of the experiments. The data collected are given in Figures 7 and 8. The consistency of the experiments from

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Figure 9. Results of isoconversional analysis for Hamaca. The effect of adding additional conversion versus temperature data is illustrated. Note that after the fourth temperature history is included, results do not change.

Figure 10. Results of isoconversional analysis for Hamaca.

one heating rate to another is of critical importance for the isoconversional analysis. The only difference between experiments should be the heating rate; other differences would be reflected in the analysis, leading to erroneous results. The analysis is applied to different subgroups of experiments in the order that they were conducted. There is no correlation in the order that the experiments were conducted. It was intended to be rather random. Starting from two experiments, additional experimental data are added and the change in the activation energy results is considered (Figure 9). Results tend to merge as the number of experiments included in the analysis increases. After the fourth run, results change little. Thus, at least five consistent experiments are necessary for the isoconversional analysis. In many cases, a sixth experiment is necessary to confirm the results. Results are expressed as a function of conversion or temperature, as shown by Figure 10. Another issue regarding the analysis is repeatability. Isoconversional analysis results for Hamaca oil are also given by our previous paper.9 Figure 11 gives the comparison. These two series of experiments are independent and conducted using completely different kinetics cells. As the figure indicates, the results are consistent. The main trends are the same. In the LTO region, the apparent activation energy decreases, achieves a minimum, and then increases up to the HTO region. A clear HTO region is observed. At the very highest temperatures, the heaviest hydrocarbons and soot are burned in both cases. 5.2. Sample A. Sample A is a 20.9° API oil. The experiments were conducted with rock samples from the original field. The

rock samples are crushed, ground, and then sieved. The experimental conditions are given in Table 6. The sample consists of 42.0 g of reservoir rock and 4.0 g of sample oil A. Thermal decomposition of anhydrous carbonates occurs in the range from 650 to 900 °C.24 Also, in the case of hydrated and basic magnesium carbonates, decomposition starts at temperatures below 600 °C.25 The analysis of rock samples indicates dolomite with no structural water.26 Therefore, no low-temperature decomposition of reservoir rock is expected. To decide the target temperature, the thermal decomposition characteristics of reservoir rock are determined. Here, the aim is to avoid any reactions associated with reservoir rock. To do so, a run is carried out with the rock sample. The results are given in Figure 12. Results indicated that, at 520 °C, CO2 started to liberate from the rock. Before this temperature, no indication of any reaction of rock with O2 was observed. Thus, the target (i.e., final) temperature is selected as 848.15 K (550 °C). Also, rock samples (for both samples A and B) are examined after the run, with no indication of reactions observed.26 Six experiments were conducted with sample A. Of these six, five experiments are found to be consistent. Figure 13 gives the experimental results. Isoconversional results of sample A are given by Figure 14. Results are quite similar to Hamaca, (25) Queralt, I.; Julia, R.; Plana, F.; Bischoff, L. A hydrous Ca-bearing magnesium carbonate from Playa Lake Sediments, Salines Lake, Spain. Am. Mineral. 1997, 82, 812–819. (26) Ross, C. M. Personal communication. Stanford University, Stanford, CA, December 2008.



Figure 11. Repeatability of the isoconversional analysis of Hamaca crude oil.

Figure 12. Thermal decomposition of reservoir rock under air.

Figure 13. Sample A: experimental data, oxygen consumption and temperature profile.

except in the region of conversions from about 0.4 to 0.8. For conversions from 0 to 0.2, a significant activation energy barrier exists that must be overcome. Reactions start at about 60 000 J/mol, and then a negative activation energy region is accompanied by a clear HTO region, with an apparent activation

energy of 50 000 J/mol. This is close to the Hamaca value of 55 000 J/mol. In general, analysis of sample A gives consistent activation energy for HTO; however, the behavior at the beginning and end of reactions should be investigated further. This crude oil/

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Figure 14. Sample A, isoconversional results.

Figure 15. Sample B: experimental data, oxygen consumption and temperature profile.

Figure 16. Sample B, isoconversional results.

rock system also needs to be tested in a combustion tube for combustion front propagation. 5.3. Sample B. Sample B is a 12° API oil. The runs with sample B were also carried out with the reservoir rock. Sample B reservoir rock is also a dolomite; therefore, the target temperature is similarly selected as 848.15 K. A total of seven experiments were conducted. Of the seven total experiments, four of them exhibit consistent behavior. For the analysis, those four experiments were used. The data are given by Figure 15. All along the experiments, the difference in the volumetric flow rate between the inlet and outlet is negligible. Therefore, 1 mol

of oxygen consumed creates 1 mol of effluent gases. The analysis results are given by Figure 16. The analysis clearly indicates LTO and HTO regions with apparent activation energies of 15 000 and 50 000 J/mol, respectively. Activation energy estimated for the HTO region is consistent with Hamaca and sample A results as well as the literature. Additionally, another region is observed at the greatest temperatures. This is indicative of the oxidation of coke and soot. In conclusion, the initial results point toward a good combustion candidate and the need for further testing in a combustion tube. Besides, the parallelism between the results


of Hamaca and sample B is of great importance. The resemblance between the shapes of the curves is a sign of a similar behavior. The main difference between the two results is the negative activation energy region that Hamaca results exhibit. 6. Conclusion In this study, the combustion kinetics of three oil samples are reported adding to the knowledge base of crude-oil combustion. The applicability of isoconversional analysis to oil oxidation is tested experimentally. Some practical aspects of the analysis are discussed. In addition synthetic examples are presented to show the diagnostic characteristics of the analysis. Isoconversional analysis applied to oil combustion naturally deconvolves multistep reactions, leading to plots of apparent activation energy versus conversion or average temperature. These plots are useful to reveal the reaction mechanism for the oxidation reactions, at present. This analysis technique and the way that it is applied in this study is only applicable to oxidation reactions. Additional methods should be applied to study the kinetics of fuel formation reactions. On the other hand, the way the analysis is applied here avoids any inconsistencies introduced by phase change. The similarities between Hamaca, sample B, and sample A results promote the idea that isoconversional analysis provides a method to characterize the burning qualities of different oils. Also, the estimated activation energies for HTO are consistent. In this study, it is shown that the analysis is repeatable and is applicable to both heavy and light oils. It is also shown that analysis provides a diagnostic plot by which cool flames are identified. Isoconversional analysis helps one to decide if the oversimplified two- or three-step treatment of crude oil oxidation is adequate or not. Although the activation energies estimated are apparent, they provide information about the complex mechanism and, consequently, intrinsic parameters. The conversion plots give clues about the underlying mechanism. Once a mechanism is proposed, activation energy and the other parameters are validated using the experimental data.

Energy & Fuels, Vol. 23, 2009 4015 Acknowledgment. Murat Cinar acknowledges the financial support of Istanbul Technical University for his doctoral studies. Additional financial support was provided by Schlumberger and the Stanford University Petroleum Research Institute Affiliates (SUPRI-A). We thank Dr. P. Hammond for suggesting the synthetic case that illustrates negative apparent activation energies and Dr. A. Burnham for suggesting the application of isoconversional techniques to oil ISC kinetics.

Nomenclature A ) pre-exponential factor (Arrhenius constant) C ) concentration Cp ) constant pressure heat capacity, J mol-1 K-1 E ) activation energy, J g-1 mol-1 F ) molar flow rate, mol/min f( ) ) reaction model k ) rate constant, units depend upon the reaction model n ) number of experiments P ) pressure q ) number of reactions Q ) heat r ) reaction rate R ) universal gas constant, J g-1 mol-1 K-1 t ) time, s T ) temperature, K T0 ) base temperature, K Ua ) overall heat-transfer coefficient times heat-exchange area X ) conversion V ) volume, cm3 Greek Letters R ) number of moles reacted per mole of fuel β ) heating rate, T/time β* ) quasi-linear heating rate, T/time ∆HRx ) heat of reaction, J/mol Subscripts A ) ambient i,j ) different experiments f ) fuel O2 ) oxygen EF900222W

Isoconversional Kinetic Analysis of the Combustion of Heavy

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