A N IN V E S T IG A T IO N O F T H E E X P L O S IO N O F A SU L
F IT E D IG E S T E R IN T H E P A P E R M IL L S A T G R A N D ’ M È R E , Q U E B E C 1
B y H . O . K e a y >
T h e circum stances surrounding the disastrous ex
plosion of one of the sulfite digesters in the paper mills
F i © . I.
of the Laurentide C om pan y at G rand’ M ère, Que., have presented a problem of no sm all interest, and it was w ith a view of determ ining so far as possible the causes leading up to this explosion th a t an in vesti
gation has been made, a t the request of the C om pan y, with the results set forth in this paper.
T h e rupture of the huge steel re
ceptacle evid en tly started in one of the three vertical seams in the mid
dle course, as indicated in F ig. x.
T h e sudden failure of the vertical seam was im m ediately followed b y an opening out of the plates along the adjacent girth seams, until the upper and low er portions of the digester were com pletely separated.
T h e prelim inary investigation im m ediately follow ing the explosion failed to point conclusively to the cause of the trouble. U p to the tim e of the explosion, no
1 W e a r e i n d e b te d to M r . T h o m a s J . K e e n a n , E d i t o r o f P a p e r , f o r th i s a r t ic l e w h ic h a p p e a r s s im u lta n e o u s ly in h is J o u r n a l.
signs of weakness in the digester were apparent. The Superintendent of the Sulfite D epartm ent had visited the digester house w ithin the hour and found e v ery
thing proceeding as usual. C h arts recovered later showed no evidence of abnorm'al conditions, such as excessive pressure, sudden opening of the relief valve, or other action recognized as p rovocative of explosion in boilers. In the operation of these digesters, there is no appreciable am ount of w ater ham m er due to the
^ )——(|^ ■ .."(j)111 (J)"
•>---0—& —b -J—q>- ^ [ ■>— o —
©-D Ł T A I L »
VtRTICAL S tA M .
F i s . 2 .
introduction of steam at the bottom . T h e digester shells were p rotected on the inside b y a lead lining, and a thorough inspection of th e ruptured seams after the explosion revealed no p ittin g from acid to account for a failure from this cause.
Jan., 19x4 T H E J O U R N A L OF I N D U S T R I A L A N D E N G I N E E R I N G C H E M I S T R Y 27
T h e usual calculations for direct stress on the seams of this digester (Fig. 2) do not indicate a stress lik ely to produce rupture.
Thus, where
P = internal pressure, taken as 100 lbs. per sq.
inch, to cover the gauge pressure, the h ydrostatic pressure of the contents, and any slight fluctuation above the normal.
r = inside radius of the digester shell = 84 inches.
t = thickness of the steel shell = 1 inch.
/ = circum ferential stress in the shell, in lbs. per sq. inch.
= = 8400 lbs. per sq. inch.
and the longitudinal stress = ^ = 4200 lbs. perPr
sq. inch.
T a k in g a single pitch length of 47/s inches on the vertical seam, the sectional area of the plates is re
duced b y rivet holes as follows:
3
*311
Shell plate, ——— = 0.6792 of full pitch section.
4-875
C over plate, ^ = 0.7308 of full pitch section.
4-875
Hence the direct stress in tension in the vertical seam becom es for the shell plate, = 12,370 lbs.
0.6792
per sq. inch, and for the cover plate ( iV a inches th ick),
For the girth seam, b y a sim ilar process, the stress in tension is for the shell plate, 6750 lbs. per sq. inch, and for the cover plate, 5480 lbs. per sq. inch; hence the circum ferential tension on th e shell plate is the greatest, and assuming an ultim ate tensile strength of plate 55,000 lbs. per sq. inch, the factor of safety
• , • 55>ooo
in tension is --- = 4 . 4 ; .
12,370
W ithin the
4
7,/s inch pitch length, there are three riv et sections in single shear. Assum ing a shearing strength of 45,000 lbs. per sq. inch in the rivets, the shearing resistance on one pitch becomes3 X 3.1416 X 1.3125 X 1.3125 X 4
5
,0004
= 182,600 lbs.
T h e load on one pitch is 8400 X 4.875 = 40,950 lbs., therefore, th e factor of safe ty in shearing the rivets
, 182,600
becomes —— — = 4.46, so the low er factor of safety
40,950 1
is apparen tly th a t in tearing the plate betw een rivets, or 4.45.
A tten tion is now natu rally directed tow ard the m a
terial of which the digester was constructed. F or the purpose of form ing an estim ate of the su itab ility of this m aterial, specimens were taken for chem ical and physical tests, w ith the follow ing results:
Ch e m i c a l An a l y s i s o p Sh e l l Pl a t e s. Di g e s t e r No. 3 C a r b o n S u lf u r P h o s p h o r u s M a n g a n e s e S a m p le P e r c e n t P e r c e n t P e r c e n t P e r c e n t
I ... . . . 0 .1 8 0 .0 1 6 0 .0 1 3 0 .3 7
2 ... . . . 0 .2 2 0 .0 1 6 0 .0 1 5 0 .4 1
3 ... . . . 0 .1 9 0 .0 1 6 0 .0 1 3 0 .4 1
4 ... . . . 0 . 2 2 0 .0 1 6 0 .0 1 5 0 . 4 0
5 ... . . . 0 .2 3 0 .0 2 0 0 .0 1 5 0 .4 1
6 ... . . . 0 .2 2 0 .0 1 7 0 .0 2 1 0 .3 7
7 ... . . . 0 .2 3 0 .0 1 8 0 .0 1 2 0 .3 5
8 ... . . . 0 . 2 0 0 .0 1 6 0 .0 2 1 0 .3 7
9 ... . . . 0 .2 1 0 .0 1 6 0 .0 1 3 0 .3 8
Ch e m i c a l An a l y s i s o p Co v e r Pl a t e, No. 2 Di g e s t e r
P e r c e n t T o t a l c a r b o n ... 0 . 3 1 3 P h o s p h o r u s ... 0 . 0 3 7 M a n g a n e s e ... 0 . 4 2 0 S u l f u r ... 0 .0 2 0
Com parison w ith th e specifications of the Am erican Society for T estin g M aterials shows th a t the shell sheet falls w ithin their recom m endations, while the cover plate fulfils the specifications except in the m atter of carbon, which is som ew hat in excess— tending to give a harder and less ductile steel than is ordinarily used in boiler work.
P h ysical tests were made at the M cG ill U niversity L aboratory, with the follow ing results:
Ph y s i c a l Te s t s o p Ma t e r i a l Fr o m Sh e l l o p Ex p l o d e d Di g e s t e r
P h y s ic a l p r o p e r tie s S p e c im e n 1 S p e c im e n 2 S p e c im e n 3 U l ti m a t e s tr e n g t h . L b s . p e r sq .
i n c h . ... 5 5 ,7 0 0 5 5 ,6 0 0 5 6 ,3 0 0 E l a s t i c lim it. L b s . p e r sq . i n c h . . . 1 0 ,7 0 0 1 6 ,2 0 0 1 6 ,9 0 0 Y ie ld p o in t . L b s . p e r s q . in c h --- 2 6 ,9 0 0 2 7 ,0 0 0 2 7 ,0 0 0 E lo n g a ti o n in 8 in c h e s ... 2 8 . 8 % 2 9 . 4 % 3 2 . 6 % R e d u c tio n in a r e a ... 5 7 . 9 % 5 7 . 9 % 5 8 . 4 % M o d u lu s o f e l a s t i c i t y ... 3 2 , 8 0 0 , 0 0 0 3 0 , 0 0 0 , 0 0 0 2 6 , 0 0 0 , 0 0 0 .
F or com parison w ith the foregoing, the follow ing tests were also m ade upon i' /s inch steel recen tly furnished for sim ilar purposes:
•
P h y s ic a l p r o p e r t ie s S p e c im e n A S p e c im e n B U l ti m a t e s tr e n g t h . L b s . p e r s q . i n c h 6 4 ,0 0 0 6 2 ,8 0 0 E l a s t i c lim it. L b s . p e r s q . i n c h ... 1 5 ,0 0 0 1 3 ,7 0 0 Y ie ld p o i n t . L b s . p e r s q . i n c h ... (a ) (a) E lo n g a ti o n in 8 in c h e s ... 3 1 . 1 % 3 1 . 0 % R e d u c tio n in a r e a ... ... 5 0 . 6 % 5 3 . 0 % M o d u lu s o f e l a s t i c i t y ... 2 9 , 0 0 0 , 0 0 0 2 9 ,0 0 0 ,0 0 0
( a ) N o p r o n o u n c e d y ie ld p o in t , b u t a g r a d u a l ly in c r e a s in g y ie ld a f t e r t h e e la s tic l i m i t w a s p a s s e d .
In both of the foregoing tests, the Am erican Society for T estin g M aterials specifications are satisfied except for the yield point, which is low. The elastic lim it, or lim it of prop ortionality of stress to strain, how ever, is v e ry low in both the old and the new m aterial, ranging from 10,700 to 16,900 lbs. per sq. inch in the form er, and from 13,700 to 15,000 lbs. per sq. inch in the latter. T h is characteristic of low elastic lim it will be brought up later in the calculation of to ta l stresses.
Subsequent investigations of the other vertical cover plates and of those rem oved from digesters of sim ilar design and service revealed cracks starting betw een the riv et holes along th e inner vertical row—
precisely where failure occurred in the ruptured seam.
T h e nature of the cracking is indicated in F ig, 3, which represents a piece of cover p late broken apart b y blow s from a sledge ham m er. T h e shaded portion
28
F i e .4.
T o exhibit this action more clearly, a one-fourth size rubber model of a section of this seam was made, as seen in Fig. 5. Fig. 6 shows a profile of the model before tension was applied, and Fig. 7 indicates clearly
c ; ( m ) . * ) '
• (® •• V
f» " . e C9 # )
s u n
F l GrS. S , C, O-Tv d.
7
the effect of tension on the seam. P articular atten tion is in vited to the concentration of bending between the inner rows of rivets, corresponding in the full size seam to a span of about 3 inches.
T h is evidence n atu rally led to a desire to determ ine, if possible, the nature and extent of the inw ard de
flection of the vertical cover plate under w orking con
ditions, and for this purpose a deflection gauge was devised, as shown in Fig. 8.
T h e fram e of the instrum ent was made from a piece of 4-inch steel channel bar. The set screws consti
tu tin g the legs are of hardened tool steel. The tw o
a t t h e le f t e n d a re p o in te d , w h ile t h e s in g le o n e , a t a d is ta n c e o f 17 in c h e s fr o m t h e fir s t t w o , is s lig h t ly r o u n d e d . T h e p o in t e d le g s a re f o r c e d in to t h e c o v e r p la t e n e a r it s o u t e r e d g e , b y lig h t b lo w s w h e n t h e in s t r u m e n t is fir s t in p la c e , so t h a t in s u b s e q u e n t r e a d in g s i t is n e c e s s a r y o n ly t o s e t t h e p o in t e d le g s b a c k in to shows the location of cracks which had started near
the rivet holes, largely on the inner side of the plate.
these little depressions to insure an exact reproduction of the original setting.
The cover plate is polished where the single rounded screw-leg rests, as are also the spots where the mi
crom eter m easurem ents are m ade.
Fig. 9 indicates the m ethod of application of the instrum ent for m easurements of deflections a t the center of th e 17-inch span. T h e m icrom eter is firm ly fixed in the center of the instrum ent fram e for this setting, and in m aking observations, the m icrom eter screw is advanced until the sense of touch lig h tly indicates th a t its point rests upon the polished plate.
In exploring the curve formed b y the deflections in the cover plate the m icrom eter was relocated a t a point 4 inches off-center, as shown in Fig. 10.
M easurem ents were tak en at intervals ranging from th irty m inutes to an hour, starting before the steam was turned on and continuing for at least half an hour after the digester was blown. The diagram , Fig. 11, which is typ ica l, presents a graphical record, on a tim e base, of the deflections observed at the center of the 17-inch span, while th at of Fig. 12 is for a point 4 inches off-center.
T h e m axim um deflections obtained in the tests represented b y Figs. 11 and 12 are replotted on the diagram in F ig. 13, on a base line representing the 17-inch span. T h e ordinates at the center and at points 4 inches off-center are plotted to a magnified scale and the sm ooth curve draw n through these points T h e g e n e r a l n a t u r e a n d lo c a t io n o f t h e s e c r a c k s
p o in t e d s t r o n g ly t o a fa ilu r e b y r e p e a t e d b e n d in g o f t h e c o v e r p la t e u n d e r s tre s s . W h ile m e a s u r e m e n ts o n t h e in s id e o f a s im ila r d ig e s t e r s h o w e d a s lig h t f la t t e n in g o f t h e c u r v e n e a r t h e s e a m , d u e p r o b a b ly t o d if f ic u lt y in t h e b e n d in g ro lls , t h is p e c u lia r it y w o u ld p r o v e r a t h e r a b e n e fit t h a n a n i n ju r y , s in c e th e t e n d e n c y o f t h e c o v e r p la t e is t o t a k e t h is f o r m a t io n u n d e r s tr e s s . T h e lin e o f r e s is ta n c e in c y lin d r ic a l s h e lls u n d e r in t e r n a l p re s s u re t e n d s to c o n fo r m to t h e c ir c le a n d s in c e t h e s in g le o u ts id e c o v e r p la t e c o n s t r u c t io n t h r o w s t h i s lin e o f r e s is ta n c e o u ts id e o f th e tr u e c ir c le , t h e t e n d e n c y u n d e r s tr e s s is t o r e s to r e i t b y b e n d in g t h e c o v e r p la t e in w a r d , a s i llu s t r a t e d in F ig . 4.
Jan., 1914 T H E J O U R N A L OF I N D U S T R I A L A N D E N G I N E E R I N G C H E M I S T R Y 29 shows the nature of the deflection. As forecast
roughly in the behavior of the rubber model, the con
centration of bending is alm ost exactly over a span of 3 inches in the m iddle portion. T he deflection at the center of the 3-inch span is found to be 0.0003 inch.
h 0 .0 6
U
* 0 .05 J I 0 0 4
„ 0 0 3
A \
/ \
/ / \
/ \\
\
T l M C IN H O U R S
9
INW ARD D E F L E C T IO N O F V E R T I C A L C O V E R P L A T C -C E N T E R O F 1 7 IN -C H S P A N
F i g . 1 1 .
VI ? 0.03 Z J O = 0 0 2
h ^0 0 01
\ \
\
Ti m e, i n h o u r* .
IN W A R D D E F L E C T I O N O F V E R T I C A L C O V E R P L A T E
-A T P O I N T - 4 I N C H E S O F F C E N T E R
Fi g. 1 2 .
Just w h y the cover plate should persist in bulging out sligh tly im m ediately after the steam was turned on the digester, following the recharge, as shown b y the negative deflection in both diagram s, was at first a troublesom e question, and called for further in v esti
gation.
Since these deflections were assumed to be the result of circum ferential stress in th e shell, it seemed reasonable to suppose th at if some sort of extension gauge were applied to the shell sheet in this region, the corresponding stress could be readily calculated.
For this purpose, a H ow ard strain gauge was applied a t the same height on th e digester as the deflection gauge, and m idw ay betw een the vertical seams of the adjacen t sheet. T his strain gauge is in reality a special m icrom eter capable of indicating w ithin 0.0001 inch error any change in length betw een tw o small carefully prepared holes drilled 10 inches apart. W here the m odulus of elasticity of steel is 30,000,000, an extension
of 0.0001 inch represents a tensile stress of 300 lbs. per sq. inch. T h is test length was tak en along the cir
cum ference, and readings were made sim ultaneously w ith those of the deflection gauge, together w ith the shell tem peratures obtained from a therm om eter sealed to the shell sheet. T h e results of these readings are shown in full lines on the diagram , Fig. 14, while the dotted lines indicate how this test length would have varied under the influence of tem perature alone.
I t was, of course, prevented from so v aryin g b y the internal pressure, therefore the distance measured up from the dotted line to the full line gives the extensions due to internal pressure.
0 .0 0 4 2
0 .0 0 4 I
0 . 0 0 4 0
0 0 0 3 9
O .O O J3
0 . 0 0 3 7
0 0 0 3 6
0 0 0 3 5
0 . 0 0 3 4
0 . 0 0 3 3
0 . 0 0 3 2
0 . 0 0 3 1
0 . 0 0 3 0
0 . 0 0 2 9
0 . 0 0 2 8
0 . 0 0 2 7
0 .0 0 2 6 0 . 0 0 2 5
O 0 0 2 4
0 , 0 0 2 3
0 0 0 2 2 0.0021 0.0020
0 . 0 0 1 9
0.00ia
o .o o n
0.0016
O .O O IS
0.0014
0 , 0 0 1 3
/
/
/
i
-/ / . . . .
7 - - V I
/ /
... J / / / . / /
\
\
\
/
--- \
- / —
/ —
T
----—
>.---\
— f
- A .
— u
\
/
/
Ti m e I N h o u r s
- S T R A I N G A U G E R E A D I N G S S H O W N IN F U L L L I N E S - C H A N G E S IN IO -IN C H T E S T L C N G T H ON S H E L L D U E T O T E M P E R A T U R E
S H O W N D O T T E D
F i o . 1 4 -,
T o exhibit more clearly w hat is going on during a single cook in the digester, a com bination diagram , Fig. 15, has been plotted w ith diagram s A, B, C, and D on the same tim e base.
D iagram A gives a graphical record of the tem peratures inside the digester, the shell tem peratures, and the tem peratures a t a point in the m iddle of the brick lining. T h e latter were obtained b y drilling a sm all hole through the shell and half w ay through the lining. Into this hole a therm om eter was inserted and carefully packed w ith fiber to isolate the bulb from outside conditions. A n im portan t feature of
30 readings, corrected for shell tem peratures as explained in connection w ith F ig. 14. T h e m axim a of the tw o
Jan., 19x4 T H E J O U R N A L OF I N D U S T R I A L A N D E N G I N E E R I N G C H E M I S T R Y 31 of internal pressure causes the shell to contract, and it therefore settles back upon the lining, which at this tim e is expanded to its m axim um b y heat. D iagram A, Fig. 15, shows the tem perature of the m iddle of the lining to be decreasing after the steam has been turned on, w ith consequent contraction, so the shell now follows the lining back until internal pressure again lifts the plate aw a y from the lining. This accounts for the curious action of the shell and cover plate for the brief period at the beginning of the cook.
W here the shell is shrinking b ack upon the lining, the latter would be expected to compress more than the form er to stretch for a given force, and it was w ith a view of determ ining the exact relation th at the moduli of elasticity of both brick and cem ent were obtained from compression tests a t the M cG ill U ni
versity L aboratory. R esults of these tests are shown in the follow ing tab le:
P h y s ic a l p r o p e r t ie s B r ic k C e m e n t
U l ti m a t e c o m p r e s s iv e s tr e n g t h . L b s . p e r sq . i n . . . 8 , 7 7 0 4 ,8 0 0 M o d u lu s o f e l a s t i c i t y ... 3 ,0 8 0 ,0 0 0 1 ,1 5 0 ,0 0 0 L e n g th ta k e n fo r e x t e n s o m e t e r ... 4 in c h e s 1 .4 in c h e s
Thus the m odulus of elasticity of the steel is about ten tim es th a t of the brick lining; in other words, a given section of brick would compress ten tim es as much as an equal section of th e shell would stretch, w ithin the elastic lim it of th e w eaker m aterial.
T O T A L S T R E S S
Proceeding now to th e calculation of m axim um stress in the cover plate, it will be recalled from the diagram , F ig. 13, th a t the m axim um deflection at the center of a 3-inch span was found to be 0.0003 inch. M aking use of the general form ula for the deflection of beam s of uniform section, within the lim its of prop ortionality of stress to strain,
A x
where
d = d is ta n c e f r o m a p o i n t o n th e b e a m t o a n y t a n g e n t.
L = le n g th o f t a n g e n t t h u s in c lu d e d . A *= a r e a o f b e n d in g m o m e n t d ia g r a m .
x =• d is ta n c e f ro m c h o s e n p o i n t t o c e n te r o f g r a v i ty o f b e n d in g m o m e n t d ia g r a m .
E = m o d u lu s o f e l a s tic ity o f m a te r ia l.
I = m o m e n t o f in e r t i a o f b e a m s e c tio n a b o u t n e u t r a l ax is.
M = b e n d in g m o m e n t ( u n if o r m in t h i s c a s e ) . f » e x tr e m e fib e r s tr e s s .
y = d is ta n c e f r o m n e u t r a l a x is t o e x tr e m e fib e r.
A =* M L , a n d x = - L 2
A x L 1 M L *
d ® - M L X X
---E l 2 E l 2 E I
2 E I d L*
M y 2 E I d y 2 E d y M «
b u t /
I L 2 1 L*
s u b s t i t u t i n g , d = 0 .0 0 0 3 L - 1 .5 E « 3 0 ,0 0 0 ,0 0 0
y = 0 .5 6 2 5
2 X 3 0 ,0 0 0 ,0 0 0 X 0 .0 0 0 3 X 0 .5 6 2 5 1.5 X 1.5
4 5 0 0 lb s . p e r s q . in c h , d u e t o b e n d in g .
A dding to this the m axim um direct stress in the cover plate, 4500 + 10,220 = 14,720 lbs. per sq. inch, the perature from the inside to the outside of the digester.
T he mean tem perature of each layer of the lining, taken from Fig. 18, was now utilized to determ ine
¡ j i s o o< 1 AO a.
5 2 1 3 0 H
zi :
ui 0 t cil ul E 3 h
<
<r
“j 1
n
2
ul I- :
A P P R O X I M A T E ! M A X I M U M - T E M P E R A T U R E S IN D l G E S T E . R L I N I N G
-F i e . 18
the am ount of expansion in each case for the entire circumference— assuming the layers free. The results of this calculation are given in the last column of Fig. 19 under the heading “ Free Extension:”
It will be noticed th a t the circum ference of the shell will extend 0.25 inch during the cook, while the average extension of the inner tw o layers of the lining would
F .g. 1 9
be 0.34 inch, if allowed to expand freely. A t the most, this would give a difference of 0.09 inch to be a c
com m odated between shell and lining in the entire circum ference of the digester. It can be readily shown th a t this has no effect, since if the shell extends 0.0024 inch in 10 inches, due to internal pressure (see diagram D, Fig. 15), then in the circum ference of the digester there would be a total extension due to pressure alone = (531 X 0.0024) -f-10 = 0 .127 inch, which lifts the shell clear of any possible crow ding b y the lining while the pressure is on.
W hen the digester is blown, how ever, the rem oval
32
m a x im u m r e p e a t e d s tr e s s o n t h e in n e r s id e o f t h e c o v e r p la t e .
R e v e r t i n g t o t h e r e s u lt s o f te n s ile s tr e s s o n m a te r ia l fr o m t h e s h e ll o f t h is d ig e s te r , a n d fr o m n e w m a te r ia l u s e d fo r s im ila r p u rp o s e s , i t w ill b e r e c a lle d t h a t t h e t r u e e la s t ic lim it s w e r e s h o w n t o r a n g e fr o m 10 ,70 0
1« 1
-. B E N D I N S M O M Ł N T D I A G R A M -.
Fi g. 2 0 .
t o 16 ,9 0 0 lb s . p e r sq . in c h . S in c e t h e t r u e e la s t ic lim it , r a t h e r t h a n t h e u lt im a te s t r e n g th , is a v i t a l
c o n s id e r a tio n in r e p e a t e d s tre s s e s s u c h a s w e a r e d e a lin g w ith h e re , t h e f a c t t h a t t h e m a x im u m fib e r s tre s s of 14 ,7 2 0 lb s . p e r sq . in c h f a lls w ith in t h e r a n g e o f e la s t ic lim it o f t h e m a te r ia l is m o s t s ig n ific a n t . N o s te e l w ill e n d u re fo r a n u n lim it e d p e r io d a r e p e a t e d s tre s s e v e n s l i g h t l y a b o v e it s e la s t ic lim it . I n t h is c a s e it t o o k fo u r t e e n y e a r s o f r e p e t it io n o f t h e s tr e s s t o c a u s e r u p t u r e , b u t t h e s a m e a c tio n is p r e s e n t in a ll d ig e s te r s o f s im ila r d e sig n — t h e s tr e s s v a r y i n g in m a g n itu d e w ith t h e t h ic k n e s s o f t h e c o v e r p la t e a n d t h e p re s s u re s c a r r ie d . W h e r e t h is s tr e s s is s h o w n t o e x c e e d t h e e la s t ic lim it o f t h e m a te r ia l o f th e c o v e r p la t e t o a n y e x t e n t w h a t e v e r , u lt im a t e fa ilu r e fr o m r e p e a t e d b e n d in g m u s t b e e x p e c te d .
McGi l l Un i v e r s i t y Mo n t r e a l, Ca n a d a