10th U.S. Na+onal Combus+on Mee+ng: Valida&on and uncertainty quan&fica&on analysis (VUQ) of a char oxida&on model Oscar Diaz-Ibarra , Jennifer Spin&, Philip Smith Ins&tute for Clean and Secure Energy, University of Utah, Salt Lake City, UT University of Utah Christopher Shaddix, Ethan Hecht Sandia Na&onal Laboratories Livermore, California April 23–26, 2017 College Park, Maryland
Char oxida+on Char oxida&on is the last stage of the coal combus&on process. It is the slower stage of the process and can take place in the whole combus&on space. Coal par(cle Drying ash Char oxida(on Devola(liza(on � • Involved in calcula&ons of temperature and gas composi&on.
Reac+ng Par+cle and Boundary Layer (RPBL) model • Computes transient-state condi&ons for a spherical, constant-diameter, reac&ng, porous Particle char par&cle and its reac&ng boundary layer. • Transport of gaseous species uses Maxwell-Stefan mul&component approach. • Homogeneous gas phase reac&ons are es&mated Bulk Flow r p with a syngas mechanism. • Heterogeneous reac&ons are calculated with a six-step reac&on mechanism. r inf • Computes carbon consump&on, uses Bha&a and PerlmuYer model to es&mate surface area Boundary layer (Bulk conditions are inputs) evolu&on. • Solves one energy equa&on for the gas and one A [ mol, cm 2 , s ] Reaction E [ kJ/mol ] 3 . 3 x 10 15 C b + C s + O 2 → CO + C ( O ) s 167 . 4 for the par&cle. 1 . 0 x 10 8 C ( O ) s + C b → CO + C s 0 . 0 • Physical proper&es depend of the frac&ons of ash 9 . 5 x 10 13 C s + O 2 → C ( O 2 ) s 142 . 3 1 . 0 x 10 8 C ( O 2 ) s + C b → CO 2 + C s 0 . 0 and carbon and on void frac&on. C s + CO 2 → CO + C ( O ) s variable 251 . 0 C s + H 2 O → H 2 + C ( O ) s variable 222 . 0
RPBL model equa+ons Energy equa+ons Transient term Kg dT g,i 1 dY k,i h i X = − [( AF cond ) i +1 / 2 − ( AF cond ) i − 1 / 2 ] − [( AF h ) i +1 / 2 − ( AF h ) i − 1 / 2 ] − V i ρ t,i + S i h k,i dt ρ t,i c p g,i V i dt k =1 Enthalpy Conduc&on Heat exchange between solid and gas 1 dT p,i h i = − [( AF cond,p ) i +1 / 2 − ( AF cond,p ) i − 1 / 2 ] − h c b ,i ˙ s c b ,i σ r,i V i − S i dt ρ bulk p,i c p p,i V i
RPBL model results Base case Particle Boundary layer 750 1880 1880 675 1760 1760 0 . 20 0 . 20 0 . 20 600 1640 1640 m 3 ] 525 Carbon bulk density [ kg 1520 1520 0 . 15 0 . 15 0 . 15 Temperature [K] Temperature [K] Position [m] Position [m] Position [m] 450 1400 1400 375 1280 1280 0 . 10 0 . 10 0 . 10 300 1160 1160 225 0 . 05 1040 1040 0 . 05 0 . 05 150 920 920 0 . 00 75 0 . 00 800 0 . 00 800 0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 0 10 20 30 40 r p [ − ] r r p [ − ] r p [ − ] r r Carbon burnout Par&cle temperature Gas temperature N= 60, Np = 30; RPBL solved 781 ODEs τ = 5 , r inf = 53 , ψ = 8 , ε p = 0 . 96 , λ p = 1 . 33 , d p = 95 µm, r p φ initial = 0 . 18 , Y c,initial = 0 . 98 , Sgc initial = 8000 [ kg c /m 2 ]
� Step 1: Selec+on of quan++es of interest (QOIs) • Par&cle temperature and velocity (experimental data collected by Hecht). • Three chars obtained from Illinois #6 (high vola&le bituminous coal), Utah Skyline (western bituminous coal), and Black Thunder (subbituminous coal). • Two environments: O 2 = (24, 36 vol%), H 2 O = (14 vol%, balance CO 2 . • Average par&cle temperature from RPBL is used.
Step 2: Input/Uncertainty Map Parameter Priority Range Nominal value min max Numerical Parameters • Sensi&vity analysis with eight ac&ve 1 15 100 30 N p N 1 30 200 60 parameters for three par&cle sizes (50 µ m, 1 1e-4 rtol Model Parameters 80 µ m , 120 µ m) ⌧ [ − ] 6 3 6 r inf • Par&cle size is the ninth parameter r p [ − ] 6 50 120 [ − ] 6 3 8 • Test sensi&vity of par&cle temperature and ✏ p [ − ] 6 0.1 1 � p [ W mK ] 6 0.1 2 velocity. ⇢ true c [ kg m 3 ] 1 921 ⇢ true ash [ kg m 3 ] 1 2000 W h solid gas [ m 2 K ] 1 1 Scenario parameters d p [ µm ] 6 50 160 v g [ m s ] 3 From reactor model • Small-size par&cles T g [ K ] 3 From reactor model 53 − 60 µm O 2 ,bulk [ − ] 3 From reactor model H 2 O bulk [ − ] 3 From reactor model • Medium-size par&cles CO 2 ,bulk [ − ] 3 From reactor model 75 − 90 µm H 2 ,bulk [ − ] 3 From reactor model CO bulk [ − ] 3 From reactor model • Big-size par&cles O 2 ,initial [ − ] 3 1.00e-3 106 − 125 µm H 2 O initial [ − ] 3 1.00e-3 H 2 ,initial [ − ] 3 1.00e-3 CO initial [ − ] 3 1.00e-3 CO 2 ,initial [ − ] 3 0.99 T p,initial [ K ] 3 From reactor model 6 0.15 0. 7 � initial Y c,intial [ − ] 6 0.5 1 Sgc initial [ kg m 2 ] 6 8000 12000 T w [ K ] 3 500 Pressure [ kg m 2 ] 3 1.00e5
� Step 2: Input/Uncertainty Map General • 256 RPBL cases were run. • Uncertainty Quan&fica&on Toolkit (UQTk) • Use coefficients of first order polynomial chaos surrogate model. d p = 80 µm (75 − 90 µm ) Par)cle temperature • Most sensi&ve parameters were � initial , Y c , and ✏ p Par&cle temperature • Next were r inf , τ and λ p r p • Least sensi&ve parameters were Sgc initial and ψ Par)cle velocity • Most sensi&ve parameters were φ initial , and Y c Conclusion • Five parameters were selected for consistency analysis: d p , � initial , Y c , ✏ p , and r inf r p Par&cle velocity
� Step 3: Experimental data collec+on Laminar, entrained flow reactor at Sandia Na&onal Laboratories. • Three types of measurements: temperature, velocity and size of a single par&cle. • Three type of char : Illinois #6 (I6), Utah Skyline (US), Black Thunder (BT). • Two environment condi&ons: � O 2 vol % = 24, 36; H 2 O vol % = 14 balance CO 2 • Six bin sizes : 53-63 µm , 63-75 µm , 75-90 µm , 90-106 µm , 106-125 µm , and 125-150 µm � Position 0 • In each posi&on approximately 100 par&cles are measured.
� Step 3: Experimental data collec+on Uncertain&es in experimental measurements Systema&c error y − y T = ∆ + β ¯ Sampling error s | β | ≤ t α / 2 ,v √ n Systema&c error is assumed much smaller than • random error. Experiment is defined as one char, one • environment, and one par&cle size at all measurement posi&ons in the reactor. Sampling error was computed for 36 • experiments using a confidence interval of 95 %.
� Step 3: Simula+on data collec+on RPBL model • RPBL was run using average temperature and velocity profiles from reactor model • Five parameters were used: d p , � initial , Y c , ✏ p , and r inf r p • Uncertainty Quan&fica&on Toolkit (UQTk) was used to produce a design of experiments. • 10901 cases were run. • Each case has 60 cells, therefore RPBL is solving 781 ODEs. • RPBL cases were run on linux cluster at the University of Utah; with 520 cores it was possible to run all cases in one day.
� Step 4: Construc+on of surrogate models • Surrogate models for par&cle temperature and velocity are created for each measurement loca&on. • PC of order 4 was used for O 2 = 24 vol %, H 2 O = 14 vol %, balance CO 2 environment; 3125 cases were run. • PC of order 5 was used for O 2 = 36 vol %, H 2 O = 14 vol %, balance CO 2 environment; 7776 cases were run.
� Step 5 : Analysis of model outputs US char O 2 = 24 vol %, H 2 O = 14 vol %, balance CO 2 environment 75-90 µm size bin φ initial • Consistency analysis was carried out for 36 r inf ∆ r p ∆ experiments performed by Hecht. • Experimental par&cle size was used as prior range. [ µm ] [ µm ] d p d p • Same set of RPBL data is used for the three chars. initial Y c,initial ✏ p ∆ ∆ | y m,e ( x ) − y e | ≤ 1 [ µm ] [ µm ] d p d p u e Parameter Prior range Consistent Nominal range value d p [ µm ] 36.9- 146.5 42.0-146.0 75-90 0.15 - 0.7 0.15 - 0.7 - � initial Y c,intial [ − ] 0.5-1 0.5-1 - r inf r p [ − ] 50-120 50-120 - ✏ p [ − ] 0.1-1 0.1-1 -
� Step 5 : Analysis of model outputs US char O 2 = 24 vol %, H 2 O = 14 vol %, balance CO 2 environment 75-90 µm size bin We performed a similar consistency analysis for the other 35 experiments and obtained consistency with all 36 experiments.
Step 6: Feedback and feed forward Model • Transient RPBL model for char oxida&on was developed. Assump&ons in the formula&on include: Diameter of the par&cle during the combus&on process was constant. Gradient of pressure was assumed negligible. Same heterogeneous reac&on mechanism was used for all three chars. • QOIs (par&cle temperature and velocity) are most sensi&ve to d p , � initial , Y c , ✏ p Consistency was found for 36 experiments if experimental size of par&cle is used as prior range. Develop models of coal devola&liza&on that predict void frac&on and carbon mass frac&on. Use a beYer classifica&on system for characterizing the size distribu&on of par&cles. • Increase the number of measurements at each posi&on in order to reduce the sampling error.
Acknowledgment • This material is based upon work supported by the Department of Energy, Na&onal Nuclear Security Administra&on, under Award Number(s) DE-NA0002375. • Center for High Performance Compu&ng at the University of Utah (CHPC). � � � �
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