Journal of Kones. Combustion Engines, VoB, No 1-2,2001 TRAP 1.0 - A ZERO DMENSONAL COMPUTER CODE FOR THE PRELMNARY ANALYSS OF SOOT REGENERATON PROCESS N DESEL PARTCULATE FLTER A. Janiszewski, Z. Nagorski and A. Teodorczyk Warsaw University a/technology, Nowowiejska 25,00-665 Warsaw Poland Tel.660-5226;fax. 8250-565; e-mail: ateod@itc.pw.edu.p/ Abstract. A computer program TRAP 1.0 was developed for the computational analysis of the pressure drop and soot regeneration characteristics of a silicon carbide (SiC) wall-flow diesel particulate filter. Diesel particulate traps are used to remove the particulates from the exhaust gas. The exhaust gases entering the channels are forced to exit through the porous walls into the adjacent channels, causing the particulates to be trapped on porous walls. The traps have very high filtration efficiencies (typically> 90%). Ceramic monolithic traps have shown great promise in control of diesel particulate emissions. This is very important for urban buses. A mathematical model, which was used in TRAP 1.0 was developed from fundamental equations, namely the conservation of mass law and the chemical reaction kinetics. The model was used to develop a time-dependent relationship which determines the particulate mass accumulated in the trap, based on engine operating conditions (exhaust temperature, oxygen concentration and exhaust flow rate) and fuel additive concentration. 1. Mathematical models 1.1 Trap mass model The model for mass has been developed from the fundamental equations, namely the conservation of mass, and the chemical reaction kinetics. The main assumptions made in the model are []: The particulate matter is consider to be mainly carbonaceous, and a simple heterogeneous reaction between the particulate matter and exhaust oxygen takes place in the trap; The oxidation rate of the particulate matter in diesel particulate trap is mainly determined by the chemical reaction kinetics; The oxygen mole fraction in the exhaust and the exhaust volumetric flow rate are constant during trap steady-state loading; The particulate layer temperature is assumed to be equal to the average trap wall temperature; Any particulate loading that takes place during the regeneration process can be neglected compared to oxidized particulate mass; Any thermal effects caused by chemical energy release have small effect on the particulate layer temperature 184
1.2 Mass balance for particulate matter The interaction between the engine and the particulate matter at time t and t+llt is shown in Figure........... to........................'.",0. '.. to,.................... Tl'll? t+llt.....", "'........................................... " ".",,"..":...................... ""...... Figure 1. Schematic ofparticulatefilter Figure 1 shows a fixed quantity of particulate matter (m) that occupies different regions at time t and a later time t+llt. The rate of change of particulate mass in the trap is given by [1]: m p (d:p ) =(m pt -(m p t" -(m p )"Xidafi". trap net particulate mass collected in the trap at time t, [g] (m p t inlet particulate mass flow rate to the trap system, [gls] (m). outlet particulate mass flow rate from the trap system, [gls] ~ P lour (m ).. rate of particulate mass oxidation in the trap; [gls]. ~ p ouaunan Both physical filtration process and a chemical oxidation process control the particulate mass. The physical filtration process is mainly dependent on: engine operating conditions; trap geometry (wall thickness, porosity, and mean pore size); particle size distribution. The chemical regeneration process is a function of following oxidation conditions: exhaust gas temperature; oxygen content in exhaust; fuel additive type and concentration. () 185
Mainly oxidation takes place in the porous wall, another oxidation is negligible. The mass flow rates of the particulate into and out of the trap can be described as: & (m p ) =Q c o ", /Jut (2) Q. standard exhaust volumetric flow rate, [m 3/s] C'o. trap inlet particulate emission concentration (engine out emission concentration) [g/rrr'] CO",. trap outlet particulate emission concentration [glm 3 ] The overall trap filtration efficiency tlr is defined as: Q (C,,, - CO",) QC,,, (3) The rate of particulate mass oxidation is given by : (m ) =m RP P oxidation P ~'0 (4) RR o overall reaction rate, [lis]. The following equation is obtained by mathematical rearrangements and with the assumption of small time period (At): - ( dmp ) dt =Q.C..11.-m RR m -' p 0 trap (5) ntegrating this equation and further mathematical operations give following equation trap particulate mass: ( Q'C'o'1Jf[ ( )~ ( )». t) RR l-exp -RRo t ~+mp, -exp -RRo t o (6) mp, trap initial particulate matter loading at time t =0, [g] t. total loading time, [s] At low values of RRo(low exhaust gas temperature and absence of fuel additive) the above equation can be expressed as: (7) 186
1.3 Reaction kinetics for oxidation of particulate matter The diesel engine particulate matter collected by the trap is of carbonaceous nature. The incomplete oxidation is assumed as follows: C + ad, -7 (2a-1)cO, + 2(1- a)co (8) Laboratory studies done by Ahlstrom [2 ] gave a value of a = 0.9 in the absence of water vapor. The oxidation rate can be described by: RR p - particulate layer reaction rate, [lis] A - p frequency factor of the thermal particulate oxidation reaction, [m 3jgls] [0,] -exhaust oxygen concentration, [g/rrr'] m - reaction order m = E p - apparent activation energy [kj/kmollk] R T p - universal gas constant 8.314 kj/kmol1k - particulate layer temperature. (9) 1.4 Reaction kinetics of the metal additive The copper fuel additive is an organometallic compound. The fuel additive is added to increase the reaction rate of the particulate matter oxidation. Mechanism developed by Pattas and Michaloupoulos [3] is as follows: 2CuO -7 Cu,O + [0] C + [0]-7 CO + Mico CO + [0]-7 CO, + Mi co, (10) The theory suggests that the metal oxides are formed in the engine by the combustion of the additives. They are then embedded in the particulate layer collected in the trap, and they initiate the oxidation of the particulate through a catalytic process. The above reactions take place are relatively low temperatures. The rate of the catalytic reaction is assumed to follow a first order (m = ) Arrhenius type equation that is given by: () RR o - particulate layer reaction rate with the additive, [lis] Au E u - frequency factor of the catalytic reaction, [m 3jgls] - apparent activation energy of the catalytic reaction [kj/kmol] 187
After summation of above equations, the overall reaction rate is given by: 1.5 Pressure drop model The overall pressure drop can be generalized for a one-dimensional flow as the sum of the pressure loss trough the porous wall plus that caused by the particulate layer. Darcy's law is given by: w - indices of wall p - indices of particulate k p w p - particulate layer permeability - particulate layer thickness (13) Overall pressure drop is necessary to know the thickness of the particulate layer. Physically measuring the particulate layer thickness is difficult since it can not be dismantled without destroying the filter structure. The particulate thickness can be calculated by the equation: m p (t) -particulate mass collected in the trap, [g] A j - trap filtration area, [m 2 ] p p - bulk density of the particulate layer, [glm 3 ] (14) The wall flow velocity can by calculated by: v =Q uet " A j (15) Q,,, - actual exhaust gas volumetric flow rate, [m1s] The following equation is obtained by substituting equations (14) and (15) into the generalized Darcy's law given by equation (13): (16) 188
The resistance parameter term is given by the following relation: (17) And equation (16) has a new formulation: (18) 1.6. Equilibrium point At the equilibrium point, the particulate mass oxidation rate equals the particulate matter deposition rate. The particulate mass in the trap (m p ") thus remains constant and result in a constant pressure drop across the filter. The equilibriumpoint is given by:.() QC'nTJt m t = --"'--'-- P RR o (19) The equilibrium point is a function of engine-out ermssion concentration, the exhaust flow rate, the trap overall filtration efficiency, and overall reaction rate. The time required for reaching the equilibrium condition: t;=_-ln(-x)) RRo (20) t - time required reaching the equilibrium condition, [s] RR o - overall reaction rate, [lis] x - equilibrium index taking values from 0 to. The equation indicates that mathematically, the equilibrium condition (x =1) will be reached at infinite time. The time required to reach 90% of the equilibrium mass can be obtained from the following equation. t~9 = R~ n(o.) o (21) 2. Computer code The computer code named Trap 1.0 based on above mathematical models was developed. The program computes time profiles of pressure drop in the filter and particulate mass collected in the trap. The profiles of pressure and mass are presented in graphical form. The user can choose one of following modes of computations: - loading with regeneration; - loading without regeneration; 189
- regeneration with constant apparent activation energy; - regeneration with various apparent activation energy. The regeneration process with constant apparent activation energy based on assumed spatial temperature profile inside the trap during regeneration. The temperature profiles are included in the parametr files. PdNlllctry 4p q. 1'.88 [!3/s) Ctn: '.5SE-GZ [glll3) eta: e.!f7, i! 110: '.WE-Z 111'S) Tep 1= 315.' [) ~._._... "W~=_ '""'M -- TeJp Z= 3l8.' [) U!Z)1-11.el g,a3) 0-.-...- [ozlz 13.88 [g,a3) f-- X: 99.8 :lt t'l Pll" C,...- j t nns~ rt)wflimll<ly i 53." g) CZM ~e.ax """Y!'"OW. t- 8.M tit) ~,-- - -~ E' e.z1e-tcl8ttj"l_u A=.28E-94 tot3t's) ~.~_.." ~~"--_.- -- -- 1) 2frt i ana paraaetrow:, Z) z", """ tellp"'ntury 3l Zmiana uykresu. 1) Me"" i ~ i1) Htnl lee, t Figure 2. The view ofprogram main computer screen with input data and calculated pressure drop and accumulated mass profiles Figure 2 presents the main menu of the program, which consists of three parts: ) list of input parameters 2) graph of pressure drop 3) graph of particulate mass collected in the trap The user can change interaclively the values of input parameters. The Trap 1.0 code has internal description on its own. 3. Results of computations. The values of basic input data used in preliminary computations are given in Table 190
Table 1. Computer code input data Parameter Description Value (Q) exhaust gas volumetric flow rate, [mls"l 10 cm (C we ) trao oarticulate emission concentration, [glm-'] 5.5e-3 eta (nf) overall tran filtration efficiencv 9.7e-1 Tempi (T."', particulate laver temperature (mode ), [K] 315 Terno2 it}'', oarticulate laver temperature (mode 2), [Kl 380 [0211 ([0 21"1) exhaust oxvgen concentration (mode ), lz/m' [0212 a0 2 ] [2]) exhaust oxvzen concentration (mode 2), z/m: 13 CU value of fuel additive (Cu) (0 for 0 ppm Cu, for 60 ppm Cu) fro (RR,,) overall reaction rate, [ls1 0.le-2 x (x) equilibrium index 0.9 nu no viscositv 0.2e-5 Af (Af) trap filtration area, [m"] 10 Kp (k n ) particulate laver permeability, [m"l 0.5e-8 rop (Po) bulk densitv of the particulate laver, [glm'l o.se-i ww (ww) wall trap thickness, lm1 0.2e-2 kw (k w ) wall permeability, [m"l 0.82e-11 The results of computations are presented in Figs. 3-7 dp Pal,, St:ratg c U!llienid u ilti'<l:c (1.1 [.. i 0.4, G.,, G.241 +03, G...!...... G., i 1 z 3 1 5 6 7 8 t. lll Figure 3 Pressure drop in loading with regeneration 191
rl,,!! 11. ------1r---t-~_+~_+~_+~+--'- l 1 '. 53.9 ~.5 35.6 26.7 rt~.-.,~lf-'. ~~~: -j-."""'-+"""""";-'_+...jl' 17,1 1 z 3 5 6 7 8 t Ol Figure 4 Particulate mass collected in the trap in loading with regeneration dp Pa Straty chnienia w f tree $.5 "'-! $.,,!,, $"34!! e,, $.17. $.85 z 3 1 5 6 7 8 tol Figure 5 Pressure drop in loading without regeneration 192
,.,..~~. 1 z 1 5 6 1 8 Figure 6 Particulate mass collected in the trap in loading without regeneration.. tfl -, -'-- ~ ' ;/.., 300. ZSl. 2:O1l. 1511 ~. 11111. t / i Sl. _.~ -- v 8El8 t [ll Figure 7 Regeneration with constant apparent activation energy 193
4. Conclusions The computer code TRAP 1.0 was developed in this work for preliminary computational analysis of regeneration process of diesel particulate trap. The code gives users information about temporal variation of two parameters: trap pressure drop and the particulate mass collected in the trap. The code is based on zero-dimensional model, which is the first step to finding more advanced models of particulate filter. This computer code and mathematical models will be advanced for the account of spatial distribution and real chemistry of soot. References 1. Awara A.E., Opris C.N., Johnson J.H.: A Theoretical and Experimental Study of the Regeneration Process in Silicon Carbide Particulate Trap using a Copper Fuel Additive, SAEPaper No. 970188, 1997 2. Ahlstrom A.F. and Odenbrand C..: Combustion Characteristics of Soot Deposits from Diesel Engines, Carbon Journal, vol 27, pp.475-483, 1989 3. Pattas K.N. and Michaloupoulos C.C.: Catalytic Activity in the Regeneration of the Ceramic Diesel Particulate Traps, SAE paper No.920362, 1992 Acknowledgement The study was supported by the State Committee for Scientific Research under the grant No. Nr 9T12D02619 194