Thermal Cracking of Norpar-13 under Near-Critical and Supercritical Conditions

Jyh-Cherng Sheu', Ning ZhoiT, and Anantha KrishnanCFD Research Corporation

215 Wynn DriveHuntsville, AL 35805

and

E. Grant Jones and Viswanath R. Katta~Innovative Scientific Solutions, Inc.

2766 Indian Ripple RoadDayton, OH 45440-3638

Abstract:

A three-step global model is developed to describe thethermal cracking of Norpar-13 under supercritical andnear-critical conditions. This cracking model isincorporated into a multi-dimensional ComputationalFluid Dynamics (CFD) code to simulate the heat/masstransfer and thermal cracking of Norpar-13 in flowsystems. The proposed model is tested against theexperimental data measured at different temperaturesand residence times. Agreement is obtained whencomparing the simulations results with measurements.The endothermic effect of Norpar-13 thermal crackingis analyzed using the validated cracking model. Theresults show that the energy absorbed by the crackingreactions has importance consequence in reducing thefuel and wall temperature although it only accounts fora small portion of total input power.

Introduction:

Aviation fuel is used as primary cooling source forremoving excess heat generated in military andcommercial aircraft. The amount of excess heat thatfuel can absorb is limited by fuel temperature. Due tothermal stability problems, the bulk fuel temperature inaircraft fuel system is restricted to 436 K [1]. In thefuture the fuel system will be operating at much highertemperature conditions (for example, 800 K) because ofthe requirements of increased thermal loads. At suchhigh-temperature environments, thermal cracking andpyrolytic deposition of fuel occur. Thermal cracking is anendothermic process that increases the fuel coolingcapacity. But pyrolytic deposition causes seriousproblems in fuel systems. It is believed that the depositformation is closely related to fuel thermal cracking.Therefore, better understanding of the thermal crackingmechanisms for jet fuels is important in order to utilize* Project Engineer, Member AIAA+ Principal Engineer, Member AIAA++ Senior Engineer, Member AIAA

the endothermic features of thermal cracking reactions.Studies on the thermal cracking of hydrocarbon

fuels have continued for several decades. Most ofthese studies were conducted under low-pressure(atmospheric) conditions due to the requirements ofpetroleum industry. Typical fuel system in aircraft isoperated under supercritical or near-critical (between3.4 and 6.9 MPa) pressure conditions [2]. Themechanisms of fuel thermal cracking under low-pressure conditions may be different from those underhigh-pressure conditions. Only a few studies were doneunder high-pressure environments [3-6]. But thosehave focused on the investigation of thermal crackingmechanisms for normal alkanes. Thermal crackingmechanisms for jet fuels under high-pressureconditions are yet to be developed.

To date, the thermal cracking chemistry ofhydrocarbon fuels (under both low-pressure and high-pressure conditions) is still unclear. Consequentially,development of detailed kinetic models for fuel thermalcracking is impossible. Alternatives such as globalchemistry models have been used to describe fuelthermal cracking. One method for developing the globalkinetic model is the lumping technique. The lumpingmethod have been employed in the petroleum industryto develop kinetic models for the (thermal and catalytic)cracking of practical fuels [7-10]. According to thismethod, species are lumped into one group and treatedas a pseudo component as the dynamic behavior ofthese species is independent of the speciescomposition [11].

In the present study, a three-step global model isproposed to describe the thermal cracking of Norpar-13under high-pressure conditions. This cracking model isdeveloped based on the lumping method that dividesthe Norpar-13/products mixture into Norpar-13, crackedn-alkane liquids, cracked 1-alkene liquids, and crackedgases. The cracking model is implemented in a multi-dimensional CFD code (CFD-ACE) to simulate theheat/mass transfer and thermal cracking of Norpar-13under near-critical and supercritical conditions. Thismodel is tested against experimental data measured at

various temperatures and residence times. Thesimulated results for all test conditions are found to beconsistent with experimental results. Based on thesesimulation results, the endothermic effect of Norpar-13thermal cracking and the relative importance of thecracking reactions are analyzed.

Experimental Method:

Norpar-13 flows in an upward direction throughSilcosteel passivated tubing [12] (3.175 mm o.d. and2.159 mm i.d) at room temperature and 1000 psia (>critical pressure of Norpar-13). The tube is electricallyheated by passing a high current through the length ofthe tube. The test duration for each run is 6 hours. Testconditions with fuel flow rate from 10 to 30 ml/min, bulkexit temperature from 843 to 873 K, and three tubelengths (0.6, 1.1, and 1.5 m) are considered in theexperiments. Wall temperatures are measured using anoptical pyrometer, cracked gas and liquid productscollected at tube exit are analyzed using gaschromatography (GC), and the quantity of deposits onthe wall surface is determined using standard surfacecarbon burn-off techniques [13].

For pure compounds like dodecane or hexadecane,fuel conversion is usually determined as the fraction ofthe disappearance of parent fuel. But for hydrocarbonmixtures like gas oils or jet fuels, this definition is notpractical. To quantify the cracking level of jet fuels,conversion is measured based on the liquid volumechange, i.e.,

Conversion = 1-- V(liquid)exi,V(Norpar13)intet

according to the definition used by Edwards andAnderson [14]. In the above equation, V(Norpar13)intel

is the volume of Norpar-13 inlet fed, and V(liquid)exlt thevolume of liquid mixture collected at tube exit.

Kinetic Modeling:

A three-step model for Norpar-13 thermal crackingunder high-pressure conditions is developed using thelumped kinetic approach. The Norpar-13/productmixture is first lumped into parent fuel (Norpar-13),cracked liquids, and cracked gases. The crackingmodel is described as

Norpar-13 -> a GasesNorpar-13 -> p LiquidsLiquids -> y Gases

(1)(2)(3)

The composition of cracked gases in Eq. (1) is adoptedfrom the experimental data measured at 12 ml/min offlow rate and 855 K of bulk exit temperature (see Table1). From our experimental observation, thecompositions of cracked gases collected at differenttemperatures and residence times are similar.Therefore, the composition of the cracked gases istreated as constant in the model. The majorcomponents of cracked liquids in Eq. (2), based on ourexperimental analysis, are n-alkanes and 1-alkenes.From this observation, the model assumes the liquidproducts are composed of n-CmH2m+2 and 1-CmH2m (6 <m < 10). The model also assumes that the 1-alkenes inthe liquid products are not further cracked into gasspecies. The above assumption is based on theargument that 1-alkenes are more likely to form 2-alkenes through isomerization reactions or to formheavier hydrocarbon through alkylation reactions.According to the descriptions above, Eqs.(2) and (3)are modified as

Norpar-13 -> |5 (n-alkanes + 1-alkenes) (4)n-alkanes -> y Gases (5)

The compositions of n-alkanes and 1-alkenes in Eqs.(4) and (5) are adopted from the experimental datameasure at 10 ml/min of flow rate and 853 K of bulk exittemperature (see Tables 2 and 3). After knowing thecompositions of gas and liquid products, the coefficienta, (3, and y in Eqs. (1), (4), and (5) are determinedbased on the mass conservation of each crackingreaction.

The reaction rates of Eqs. (1), (4) and(5) areassumed to follow the first-order, Arrhenius-typekinetics, i.e.,

-d[Norpar-13]/dt = k, [Norpar-13]-d[Norpar-13]/dt = k4 [Norpar-13]-d[n-alkanes]/dt = k5 [n-alkanes]

andk1=A1e(-El/H"T)

If _ A 0(-E4"VO-

Norpar-13 in Eq. (1), based on our analysis, is made upof 0.7 wt% undecane, 15.0% dodecane, 51.3%tridecane, 32.3% tetradecane, and 0.7% pentadecane.

(6)

where k: (i = 1, 4, and 5) is the rate constant, A, the pre-exponential factor, E, the activation energy, Ry theuniversal gas constant, and T the reaction temperature.The rate constants k, and k4 are estimated by linearcombination of the rate constants for the thermalcracking of pure compounds. The cracking rates of thepure compounds are adopted from the correlation of Yuand Eser [15]. The calculated pre-exponential factorsand activation energies are

A, = A4 = 3.64x1015(1/s)

andE, = E4 = 63 (kcal/mole)

The linear combination method; however, can not beused to estimate the rate constant k5 due to the lack ofinformation on the cracking rate of n-C6H14 and n-C7H16

under high-pressure conditions. The kinetic correlationin [15] is only good for the range n-C10H22 - n-C^H^, andextendible to the range n-C8H18 - C^H .̂ For simplicity,k5 in the current model is approximated as the rateconstant of n-C8H18 thermal cracking. Using thecorrelation in [15], A5 and E5 are calculated as5.34.x1011 (1/s) and 52.4 (kcal/mole), respectively.

Table 1. Composition of gas products from Norpar-13thermal cracking

Compound

hydrogenmethaneethyleneethanepropylenepropane1 -butenen-butaneunidentified

ChemicalFormulaH2

CH4C2H4C2H6C3H6C3H8C4H8C<H10

c;'

Vol. %

1.9910.6412.8116.4718.1913.7313.85

1.8610.46

* The unidentified C5+ is assumed to be 1-pentene in

the model

Table 2 Composition of n-alkanes liquid products fromNorpar-13 thermal cracking

Compound Chemical Formulan-hexanen-heptanen-octanen-nonanen-decane

C6H14C7H16C8H18C9H20C10H22

Vol. %34.9525.4816.4613.56

9.55

Table 3 Composition of 1-alkenes liquid products fromNorpar-13 thermal cracking

Compound Chemical Formula1 -hexene1-heptene1 -octene1-nonene1-decene

cKcX]

Vol. %31.4324.1618.6014.1511.66

Numerical Method:

The thermal cracking model described above isincorporated in CFD-ACE, a commercial computationalfluid dynamics software developed by CFD ResearchCorporation. Numerical simulations of Norpar-13thermal cracking in flow systems are then performedusing the modified CFD-ACE code. In the simulation,fluid motion in the tube is assumed to be axisymmetricand in steady-state. The flow is assumed to beturbulent, and is simulated using the standard k-emodel. The fluid properties of the Norpar-13/productmixture are estimated using SUPERTRAPP [16]. Forthe thermal boundary conditions, uniform and constantheat flux is applied along the tube wall. The heatingpower used in the simulation is 10-15 % lower thanexperimental value to account for the heat loss from theconnection between electrical terminal and fuel tube.Because the wall temperature considered in the studiescan be as high as 950 K, radiation and convection heatloss can not be neglected. The heat loss from radiationis estimated by the Stefan-Boltzmann law and that fromconvection by Newton's law of cooling, i.e.,

= q«mv + qra<i = h(Twall - TJ + ea(T*all - (7)

where q^ represents the total heat loss, qrad theradiative heat loss, qconv the convective heat loss, T ,̂,the wall temperature, T^ the surrounding temperature,a the Stefan-Boltzmann constant, e the emissivitydetermined from experimental calibration, and h theheat transfer coefficient determined from the correlationof Churchill and Chu [17].

Results and Discussion:

Heat Loss Evaluation:

As mentioned earlier in last section, the heat loss tothe environment is not negligible in the current study.Therefore it is important to know the heat loss amountduring the experiment in order to correctly predict theendothermic effects of fuel thermal cracking. Theamount of heat loss is determined experimentally bycomparing the powers used to heat insulated and non-insulated tubes. The test is performed using a 0.6-mtube with inlet flow rate of 10 ml/min and bulk exittemperature of 843 K. The measured powers forheating insulated and non-insulated tubes are 346.2and 463.5 W, respectively. The fraction of heat losswith respect to the input power is calculated as 25.3 %.

The evaluation of heat loss is also performednumerically by simulating the test cases describedabove. The non-insulated case is simulated byincluding both thermal cracking and heat loss models in

1000

Exp. Data(1)Exp. Data (2)

Exp. Data (3)Cracking Model

Non-Cracking Model

3000 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Axial Distance (m)

Figure 1 .Axial distributions of wall temperaturecalculated using a 0.6-m tube with flow rate of 10ml/min and bulk exit temperature of 847 K.

1000

900

.800

500

400

300

0

A

D

Exp. Data (1)Exp. Data (2)Exp. Data (3)

- Cracking Model- Non-Cracking Model

0.2 1.2 1.4 1.60.4 0.6 0.8 1Axial Distance (m)

Figure 3. Axial distributions of wall temperaturecalculated using a 1.5-m tube with flow rate of 10ml/min and bulk exit temperature of 848 K.

1000

900 -

Data(l)Data (2)Data (3)

Cracking Model

Non-Cracking Model

0 0.2 1 1.20.4 0.6 0.8Axial Distance (m)

Figure 2. Axial distributions of wall temperaturecalculated using a 1.1-m tube with flow rate of 10ml/min and bulk exit temperature of 847 K.

1000

900 -

Exp. Data (1)Exp. Data (2)Exp. Data (3)Cracking ModelNon-Cracking Model

0 0.2 0.4 1.2 1.4 1.60.6 0.8 1Axial Distance (m)

Figure 4. Axial distributions of wall temperaturecalculated using a 1.5-m tube with flow rate of 12ml/min and bulk exit temperature of 855 K.

the calculation, and the insulated case is simulated byincluding only the thermal cracking model in thecalculation. The calculated powers for heating theinsulated and non-insulated tubes are 325 and 460 W,respectively, comparing favorably with the experimentalvalues above.

Cracking Model Validation:

Six test cases with flow rate from 10 to 30 ml/min,bulk exit temperature from 847 to 871 K, and tubelength from 0.6 to 1.5 m are simulated. The calculatedwall temperature distributions and fuel conversions arecompared with experimental data. Figures 1-6 show the

distributions of wall temperature obtained fromcalculations and measurements for the six test cases.In the figures, the circle, triangle, and rectangularsymbols represent three sets of experimental datameasured at different times during the sameexperiment and the solid line represents the simulationresults. For all cases examined, the simulated walltemperatures match experimental data bothqualitatively and quantitatively. The calculated andmeasured conversion values for the six test cases arelisted in Table 4. Except Test Case 6, the predictedconversion values agree well with experimental data.The reason to cause the difference between thecalculated and measured conversions for Test Case 6is not clear at the current stage. It may either attributeto the limitation of current model in simulating higherflow-rate conditions, or the uncertainties ofmeasurements.

Table 4. Measured and calculated conversion values

Test Test Conditions * Conversion (%)No. (ml/min) (K) (m) Measurement Calculation123456

101010122030

847847848855868871

0.61.11.51.51.11.1

16.015.022.033.023.010.5

15.015.620.529.223.018.0

* The test conditions in orders are inlet flow rate, bulkexit temperature, and tube length.

Endothermic Effect of Thermal Cracking:

The amount of heat absorbed by the thermal crackingreactions (i.e., endotherm) can be determined byanalyzing the energy balance on the heated tube.Following Sobel and Spadaccini [18], the endotherm,Qendo, is expressed as

^endo ^ens (8)

where Qin represents the input heating power, Q^ theheat loss, and Q^ the sensible heating used to raisefuel temperature. Qln is determined by measurements,and Qsens and Q^ are estimated based on simulationresults. The values of Qendo/Qin and Q^Q;,, calculatedusing Eq. (8) are listed in Table 5. For the six casesexamined, the calculated endotherm is significantly lessthan the heat loss, confirming the requirement ofconsidering heat loss in the current study. Theendotherm, although not as significant as the heat loss,has important consequence in reducing the fuel andwall temperatures. This can be demonstrated bycomparing the simulation results predicted by the

cracking and non-cracking models. For the six casesstudied, the bulk exit temperatures predicted by thenon-cracking model are 50-80 K higher than thoseobtained by the cracking model (see Table 6).

The endothermic effect on the wall temperature isstudied by comparing the axial distributions of walltemperature predicted by both models. The simulationresults for the six cases are shown in Figs 1-6. Theresults of Test Case 1 (see Fig. 1) are discussed asfollows. In the upstream region (i.e., from tube inlet toaxial distance of 0.5 m), the wall temperaturespredicted by both models are almost identical. Thissuggests that the endothermic effect of thermalcracking reactions is negligible because the fueltemperature in this region is too low. In the downstreamregion (i.e., from axial distance of 0.5 m to tube exit),the wall temperature calculated by the non-crackingmodel becomes increasingly higher than that by thecracking model as the axial distance increases. At thetube exit, the wall temperature calculated by the non-cracking model is observed to be 52 K higher than thatby the cracking model. Similar trends are also observedwhen comparing the simulation results for theremaining five test cases (see Figs 2-6). The predictedexit wall temperatures by the non-cracking model are43-74 K higher than those by the cracking model forTest Cases 2-5 (see Table 6).

Table 5. Calculated endotherm for Norpar-13 thermalcracking

Test No." QenJQ,n (%) QfoJQin (%)123456

9.28.38.7

11.612.511.5

29.031.443.646.724.519.1

* The test conditions are the same as those in Table 4.

Table 6. Bulk and wall exit temperatures calculated byendothermic and non-endothermic models

TestNo.'123456

EndothermicTbulk(K) Twall(K)

860850850875890891

906868860888921931

Non-EndothermicTbulk (K) Twall (K)

914900900942970963

958911903947995998

' The test conditions are the same as those in Table 4.

1000

900

1 700

500

400

300

oA

D

Exp. Data(1)Exp. Data (2)Exp. Data (3)

- Cracking Model- Cracking Model

0

Figure 5.calculated

0.2 0.4 0.6 0.8Axial Distance (m)

1 1.2

Axial distributions of wall temperatureusing a 1.1-m tube with flow rate of 20

Exp. Data (1)Exp. Data (2)Exp. Data (3)Cracking Model

----- Non-Cracking Model

300

0.2 1 1.2

ml/min and bulk exit temperature of 868 K.

0.4 0.6 0.8Axial Distance (m)

Figure 6. Axial distributions of wall temperaturecalculated using a 1.1-m tube with flow rate of 30ml/min and bulk exit temperature of 871 K.

Parametric Study of Cracking Reactions:

Parametric study of the three cracking reactions isperformed to examine (1) the relative importance of theprimary and secondary cracking, and (2) the relativeendothermic performance of the cracking (from Norpar-13) to gases and to liquids. Three cracking models areused in the parametric study. The first cracking model(denoted as Model A) considers only the first-stepreaction, i.e., Eq. (1), the second model (denoted asModel B) considers the first- and second-stepreactions, i.e., Eqs. (1) and (4), and the third one is thepresent three-step cracking model.

The relative importance of the primary andsecondary cracking is studied by comparing the bulkexit temperatures calculated by Models B and thethree-step cracking model. As illustrated in Table 7, theexit temperatures calculated by the two models arealmost identical. This comparison suggests that thesecondary cracking from n-alkanes to gases isnegligible. This result is not surprising since thereaction rate of secondary cracking used in the three-step model is much smaller than those of primarycracking. As suggested by Yu and Eser [15], heavieralkanes can accelerate the cracking of lighter ones inthe thermal reactions of n-alkane mixture. If thishappens in our tests, re-calibration of secondarycracking rate in our model will be required.

The relative endothermic performance of thecracking to gases and to liquids is analyzed bycomparing the bulk exit temperatures predicted by

Models A and the three-step model. From Table 7, thebulk exit temperatures calculated by the three-stepmodel are only 5-7 K lower than those obtained byModel A. As discussed earlier in last section, theendotherm of Norpar-13 thermal cracking results indecrease of bulk exit temperature by 50-80 K. Thisindicates that the cracking to liquids only has minoreffect in reducing fuel temperature. Most of theendothermic effect comes from the cracking to gasproducts.

Table 7. Bulk exit temperatures (K) calculated by ModelA, Model Ba, and current the three-step cracking model.

Test No.b123456

Model A866865855881896898

Model B860850850875890891

Three-step860850850875890891

a Model A includes only the first-step reaction andModel B includes the first-step and second-stepreactions in the cracking model,b The test conditions are the same as those in Table 4.

CONCLUSION:

A three-step global model is proposed to describethe thermal cracking of Norpar-13 under supercritical

and near-critical pressure conditions. The crackingmodel is developed based on a method that lumps theNorpar-13/product mixture into Norpar-13, cracked n-alkane in liquid phase, cracked 1-alkene in liquidphase, and cracked gases. The cracking model isincorporated into a multi-dimensional CFD code tosimulate the heat/mass transfer and thermal cracking ofNorpar-13 in flow systems. This model is tested againstexperimental data measured at different flowtemperatures and residence times. The simulatedtemperature and conversion values agree well withexperimental data.

The endothermic effect of Norpar-13 thermalcracking is studied using the validated cracking model.For the conditions studied, the calculated endothermonly absorbs about 10% of input power. The calculatedendotherm, although not as significant as the heat lostto the environment, has non-negligible effect inreducing fuel and wall temperatures. Our studies showthat the endotherm of Norpar-13 thermal crackingresults in decreases of bulk exit and wall exittemperatures by 50-80 K and 43-74 K, respectively.The relative endothermic contributions of the cracking(from Norpar-13) to gases and the cracking to liquidsare analyzed using the parametric study on the threecracking reactions. The simulation results show thatmost of the endothermic effect comes from the crackingto gases. The cracking to liquids only plays a minor rolein increasing the fuel cooling capacity.

Acknowledgments:

This work is supported by an AF contract (#F33615-96-C-2619). The authors thank Mr. EdwinCorporan, the project monitor, for his support of thiswork. The authors would also like to thank Dr. MelRoquemore and Dr. Tim Edwards of Wright Laboratoryfor their guidance during the course of this work.. Theanalysis of the cracked gas and liquid products wereperformed by Mr. Rich Striebich of The University ofDayton Research Institute. The experimental efforts ofMr. Walt J. Balster (ISSI) and Ms Lori M. Balster (ISSI)are acknowledged.

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