C SOUTH EST
FOREST SERVICE
U. S.DEPARTMENT OF AGRICULTURE
P. O. BOX 245, BERKELEY, CALIFORNIA 94701
COMPUTER TECHN
COMBUST ON OF CELLULOSE and other
Andrew M. Stein
USDA Forest Service
Research Note PSW-266
1972
Absfmcd-:A computer method has been developed for
~ u l a t h gthe combustion of wood and other cellulosic fuels. The products of combustion are used as
hput for a convection model that slimulates real fires.
The method allows the chemical process to proceed to
equilibrium and then examines the effects of mass
addition and repartitioning on the Ruid mechanics of
Ihe convection column in a fire.
stion; combustion prodputer programs; shula-
Brka
W.Bauske
Work on modeling a convective fire has been
hampered until recently by the lack of a method to
partition products of cellulosic combustion. Such a
method is needed to develop data for input in a
computer sirnulation of a real fire. We have now
developed such a techique. It can simulate the
combustion of wood and other fuels composed of the
carbon, hydrogen, nitrogen, and oxygen atoms. The
products computed can be used to specify the average
molecular weight of gases injected into the lower
boundary of a convec"con model and then transported into the con~sectioncolumn. The computer
solves the governling differential equations of mass,
energy, and momentum consemtion. The amount of
water vapor, carbon d i o ~ d e ,and other gases produced by a fire is large e n o u b to make the molecular
wei&t of the convection column sipificantly different from that of the ambient air. The method
developed can account for this difference. It allows
the chemical process to proceed to equilibrium and
then examines the effect of mass addition and
repartitioning on the fluid mechanics of a convection
column.
This note describes the analysis and sirnulation
techique, and shows how the input requirements for
a convective model can be specified. The following
supplements to this note are available upon request to
the Director, Pacific Southwest Forest and Range
Experiment Station, I$. 0.Box 245, Berkeley, California. 94701. Attention: Computer Services Librarian:
Instructions for using the computer pograms.
Computations of the equilibrium composition
of end products of wood and other fuels for specified
stoichiometric conditions.
CHEMICAL EQUILIBRIUM
The equilibrium states represent a limiting condition, and for any considerations of chemical reactivity, the equfiibriurn solution m s t first be h o w n . In
-
k&-temperataare combustion processes, the kinetics
of important reactions are fast, Consequently, the
criteria as set forth by the van9tHoff reaction isocore,
Gibbs-Helmholtz equations, Harn3ton9sprinciple, and
st atistical mechanics apply. C h e ~ c a l thermodynamics require that for a speciGed system in
equfiibrium there is a unique composition. Any
departures from ewfiibrium at Kgh temperature
represents a perturbation of the equgibrium states.
Therefore, it is necessary to obtain "ce appropriate
equfiibrium solution before studying the non-equilibrium periturbations. The equilibrium state is specified
from knovvledge of "ce atomic composition along
with the specification of any two state variables or
thermodynamic properties.
This approach has been used successfully in the
analysis and performance of liquid and solid rocket
propellants1 ; evaluation of explosives2 ;and to develop techniques for measuring Egh temperature, pressure, and the kinetics of complex chemicd react i o n ~ . It
~ has also been successfully applied to
photolytic and atmospheric processes, and to the
development of materids for solid state electronics
systems.
The thermochernical data in our analysis were
derjived from the ~ ~ i n " ~ r r n y - ~Force
a ~ -thermo~ir
chefical tables." h d thermochemical data for the
more complex species, such as the aromatic hydromrbons and their deriatives, were taken from the
h e r i c a n Petroleum Institute t h e r m o c h e ~ c d tab l e ~ The
. ~ standard state was taken as 298.1G°K. and
1 atmosphere pressure. AH,,,
for an species was
abitrarily taken as zero. The computer searches both
sets of data and selects all species wKch are likely
reaction products in a @ven system.
The composition of the major species was deter~ n e "&heoretically
d
by solving the approximate massaction equations or dnimking the free energy of the
system subject to the constraint of atom consemat i ~ n T.h~e chemical reactions can be expressed as:
The mass-action expression for the j'th reaction of
Lhis set is shown in Equation 2:
A set of linear equations was derived by t&ng the
l o g a r i t h of the mass actions expressions for each of
the n reactions of Equation 2, expanding the resultkg
functions in a Taylor series, and rejecthg all nonEnear terms. The resulting set of equations is:
in wkch F(X) is the total free energy change in the
system, !
X is the mole free energies for the i9th
gaseous species,
is the mole free energy of the k9th
condensed species, and C! and $ are the compositions of the i'th and k9"c chefical species at
equfiibrjium.
The set of linear equations was solved by the
computer by using an ikratile techflique. To obtain a
u-nique solution, it was necessary to h p o s e the
constraht of atom consemation:
in wfich a*-is the number of atoms in the gaseous
species, anfake,is the number of atoms of condensed
J
.species.
USE OR APPROACH
The success of this approach depends on the
extent to wEch equgibrium is acEeved; the hclusion
of all important chemical species; the correctness of
the thermochemical data; the validity of linearizhmzg
the mass action equations, and solving the resulthg
kinear set; and the capamity of the computhg
faclility, i.e., the ability to maintain precision in
calcdations wherein successive operations are performed on extremely large and small numbers.
One way to assess the extent to wbch these five
criteria are d i d is to compare the test results with a
computed solution. For many rocket performance
studies,' q 2 the ageement between experiment and
&eory has been excellent.
This approach has proved useful in shulating the
combustion of cellulose and other fuels, but realistic
experiments vvould be necessary to determline the
extent to wluich simulation results are valid.
For the fuel correspondhg to wood, the composition expressed as urei@t iFraction was:
C,H1 ,O, (alpha cellulose)
C,H, 0, (hemicellulose [pentosan] )
C, H, 0, (lignin)
So&um (arbitrarily added)
Potasslium (abitrarily added)
,,
0.54
.24
.20
-01
.0 1
We found that combustion in the presence of less
than the stoiclhiometric m o u n t of oxi&er produces
significant equilibrium concentrations: of intermediate
products or pollutants or both. These observations
apply to the entire range of temperature and pressure
hvestigated, and to each fuel system.
COMPUTER PROGUM
The computer program we dewloped is an adaptation of two other progrms for calculating the
cheficd equilibrium composition written by Gordon
md ~ c ~ r i d e .These
'
are called GECS and ODE. In
most versions avagable, CEGS is written in Fortran HV
for operation on the IBM 7090 computeragWe have
adapted a version called the C E S C ~ Oto~the IBM 360
computer.
n
The CIEglS70 version consists of a m ~ program
md 19 subroutines. One is a du
(possibly a p r o ~ s i o nfor a subroutine yet to be
witten) and six are used only for calculation of
theoretical rocket performance-they may be resubroutines to speed cornnilation
t h e . We have found that cowgation time can be
considerable, as the progrm fills about 3,000
punchcar ds .
NOTES
browne, H. N.,Mary M. Wgiams, and D. R. Cruise. 7%
theomtical comput b n of equilibrium compositions, thermodynamic poperfies and performance characteristics of pmpllant systems. U S . Naval Ordnance Test Stn. Rep. NOTS
TP-2434, 61 p. 1960.
Doizegan, A. J. and M. Forbeer. Solution of thermochemical
propellant calculations on a hi@ speed dign'l.uk computeE Jet
Propulsion 26: 164-1731, 1954.
Tsao, C. C,, and 6. Wiederhold. Kine~csequzbvaiurn and
performance of high tempemture systems. Proc. 2nd Conf.
High Temperature Systems 1962: 261-269. 1963.
2 ~ a m k k i ~ l eG.,
r , and R. Edse. The composifiion of dissocating combustion gases and the calculation of simultaneous
equilibui~.Z. Elektrochem. 49: 178-186. 1943.
'~erker, H. J. The calmfation of equilib~urnflame gas
composi~ons.J. Inst. Fuel 40: 206-213. 1967.
Nawsocki, P. J., and R, Papa. Atmcasphefic processes.
G""~h~"i""or~. Am- Final
GCA 41-37-A, 706 P1961.
Ellis, E. E., Bnd G. S. B&n. En@neeP-iMg selectI'on of
reac~onrate constants for gaseous chemical species in high
&mperatures. Western States Sec. Combustion Inst. WSS/GI
Paper 62-27,141 p. 1962.
" ~ n o n ~ m o u s J. ' N A F thermochemical fables. Midland,
Mich.: Cow Chemical Co. series A-June 1963; series
B-January 1964; series C-April 1965; series D-March 1966;
series E-Januuy 1967.
'~ossini, Frederick ID., et al. Selected values of physical and
thermodynamic properties of hydvocarbons and related
compounds. API research project 44. Pittsburgh: Carnegie
Press. 1953.
'~eleznik, I?. J., and S. Gordon. An analytical investigation
of three general methods of calculativng chemical equilibrium
compositions. Lewis Res, Center NASA TN-D 473, 35 p.
1960.
White, W. B., S. M. Johnson, and 6. B. Dantzig. Chemical
equilibrium in complex mixtures. J. Chem\. Physics 28 : 5,
1958.
'Gordon, S., and B. McBride. Preliminary &scriplion of
CECS70, a computer program for calculatkg the chemical
equi2t'bp.iumcomposition with applications. 10 p. 1970.
Gordon, S., and B. McBride. Pveliminavy description of
ODE, a computer program for the calculafion of chemical
equiEibp.iumcomposition with applications. 9 p. 1968.
Gordon S., and B. McBride. eeliminary description of
ODE, a computer progam for the calculation of chemical
equilibrium composition with applications. 10 p. 1968.
(Unpublished reports on file at Lewis Res. Center, U S A ,
Cleveland, Ohio.)
8 ~ e ~ z n i Frank
k,
J., and Sanford Brown. A genepal IBM 704
7090 computer program fir computation of chemical
equilibriu m compositions, rocket performance and
etzapman -JouqtaeL detonations. NASA Tech. Note D- 1454,
Lewis Res. Center, Cleveland, Ohio, 149 p. 1962.
CPY
Gordon, Sanford, and Frank J. Zeleznik. A general IBM
704 or 7090 computer progam for computation of chemical
equ ilibriu m compositions, rocket perhrmance and
Chupman-Jouquet detonations. Supplement 1-assigned area
ratio performmce. NASA Tech. Note D-1737, Lewis Res.
Center, Cleveland, Ohio. 78 p,, 1963.
The Authoxs
are assigned to research in mass fire systems, with headquarters at the
Station's Forest Fire Laboratory, Riverside, Calif. ANDREW M. STHN, a
research physical chemist, emned an A.8. degree at Texas College (1940)
and an M.S. in physical chemistry at State University of Iowa (1942). We
joined the Station staff in 1969. B H A N W. BAUSKE, a mathematician, is
a 1969 mathematics graduate of the University of California, Riverside. He
became a member of the Station staff that same year.
-
The Forest %mice of the UeSaDep
. . . Conducts forest and range research at mose than 75 loca~onsfrom Pue&o Rim to
Alaska and HawAi.
. . . Participates with all State forestry agencies in cooperative programs to protect and hprove eke Nation's 395 maion acres ofState, Bwal, and private forsst Iands.
. . . Manages and protects the 187-million-acre National Forest System for sustained yield
of its mmy products and services.
Tk Pacific Southwest Forest m d Rmge Experiment S t a ~ s n
represents the resexch brmch of the Forest Service in California and Hawaii.