ML19275A957

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Technical Staff Analysis Rept on Core Damage,To the Presidents Commission on the Accident at Tmi
ML19275A957
Person / Time
Site: Crane Constellation icon.png
Issue date: 10/31/1979
From: English R
PRESIDENT'S COMMISSION ON THE ACCIDENT AT THREE MILE
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ML19254E707 List:
References
NUDOCS 7910300408
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{{#Wiki_filter:.% TECHNICAL STAFF ANALYSIS REPORT ON CORE DAMAGE TO PRESIDENT'S CO>SIISSION ON THE ACCIDENT AT THREE MILE ISLAND ADVANCE COPY NOT FOR PUBLIC RELEASE 3EFORE AMs, NEDNESDAY, OCTOBER 31, 1979 79/03o408 1183 008

TECHNICAL STAFF ANALYSIS REPORT CORE DA.'-! AGE by Robert E. Engl_sh TECHNICAL ASSESSMENT TASK FORCE Cctober 25, 1979 Washing:cn, D.C. 1183 309

This document ii solely the work of the Commission staff and does not necessarily represent the views of the Free 4 dent's Cornission or sny Terter of the Cornission. This pre-publication copy is a final document and will be subject only to minor editorial changes in its published fsrr.. 1183 010

1 SUSCIARY AND FINDINGS In assessing core damage, three basic yardsticks were used: (1) An inventory of all the hydrogen released was ased for estimating the degree of oxidation of the circonium (ref. 1). (2) The measured fission products released to the reactor coolant and to the atmosphere of the containment building were used to infer fuel peak temperatures reached (ref. 1). (3) The thermal-hydraulics (ref. 2) of the reactor loop ~over the first 3.5 hours were analyzed by means of the TRAC computer code (ref. 3-4). This produced a temperature history that would somewrat underestimate both the hydrogen generation and the cuantity of gaseous fission products released. References 5 and 6 are two early estimates of core damage by NRC. Reference 7 desc.ibes the processes and extent of core damage and c.ives a. chv.sical cicture of the nature and location of the various tvees of damace. More rigorous analysis (refs. 3 and 4) produces results in general agreement with the results presented in reference 7. The following findings wer eached: (1) Reference 17 specifies that power-generating nuclear reactors shall be designed to remain within the followir.g limits: (a) Peak cladding temperature shali not exceed 2200 F. (b) The zirconium cladding oxidized shall not exceed 17 percent of cladding thickness. (c) The total amount of hydrogen generated from the zirconium-water reaction shall not exceed 1 percent of that producible by oxidizing all of the fuel cladding. At TMI-2, all these limits were exceeded. (2) Ninety cercent or more of the fuel rods have t rst. (3) A hydrogen inventory indicates that 44-63% of all the circonium in the reactor has been oxidized. The apper 60-70% of the zirconium clad is so embrittled that it has lost its structural integrity. (4) Fuel temperature exceeded 3500 F throughout the upper 40-50 percent of the core. Fuel temperature may have exceeded 4000'F throughout 30-40 percent cf the core /olume. 1183 011

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m..". 7

?.." u...o ~e _..e - a.' a c,. e-a_...a_.. *- o a- . ". a a."s. s "... o '...k. e a 1.4 ue#'+- 4 n. ^ e ~ o.-... 4. a *- 4 c n. o.' _.k a =w"-.. o' .'"a.1 14~"a#4 3 4 -m u n --=------ n. m..y r _,-. ." _= - av. a 4 "m a - *. "- =.1 .i..s-a - ^. ^# _"e -a=^~o. _#"_a1 y-----. ltselr_. (6) Continuing leaching of radioactive Cs, I, Sr, and .nto the reactor's cooling water indicates that some of a-w - - e. 4-4.,. 4.. e ' ", d4 v.4 A ed. # ^. ~. a. e -..a a - m (7) .r o...me4>- c "..n.c e d - =_ a A 4.. w~ s o = " v -.". .w..e 4 -c .n. ,^ 2 a se'.' cua-=^ .A - a ~ =-v-c r-svu ca n..v-z_ .an"-"n An_a___ .c- -a a ,2s m.4nm-es,.: a.- o m, _-. o.: .wm..e ac

_Aane,

_= v.o r s - nn-lea- ~ -u 3 a-- Safety Analysis Center surmises that a section of the core suddenly slumped downward as a consecuence of earlier damage (ref. 3). The staff acrees. (8) In the hottast portions of the core, sections of the control rods probably melted. Because the constituents c.#

  • k.e.ods a.e e oe".~-4a'1":.'.so-bla 4.".
v. a
  • o -,

"."..o. " o_ ".. m.. - i" a poisons the rods contained are very likely still in the ; ore (rer..). a (9) According to reference 9, slumping of the core (as In e acove) increases core reactivity,.out the core is nct close to becominc. critical. Even if the core slumes to its point of greatest reactivity and even if the neutron c.oisons in the control rods are somehow removed from the core, the core can be kept subcritical 4" its cooling water contains at least 3180 parts of boron per million parts of water (by .,a 4 .w. ). ota*an -m. son .4-ra;- u-- a a.4.,.e .; n.; n g .- a s e u-., neu.vr a .v - 3. n-e s 3500 parts per million by adding boric acid (ref. 9). INTRODUCTION For core damage, a crucial pericd was the time interval o." 10.' t' 10 -...i.nu.e s "-mm st.a. o.# "..".a a - - 4 d o.. *-. D u 4..~, .".4- ..u a .e 4od, c o.i t..- m.:.he -a_ac.o. ,a-o .-,a y t a_ A

o. -

v y v .-otracted ceriod, temceratures rose to hic.h levels, and su,hs an~4a.1. A a.., c a .o w.w.a -n.-aaus ..w. a. r e_ a-u,.1.. .2-3- -v r...: c.r.am _.; n n c,. e e. ~. a..n. +. m: v o e a_ A.,....a a s ~_ a..m s .-na m u n s -~ - a s y

    • ea. -.'..c.4 ^ a _l sv^u es, v.i

's.' ) a.n i.nve u- ~ o -"; ^# ..".a. y e v. w y d. o c, e.. .- n p. o - a A .s y._.u. a.GaC_.io. a# k.^*_ ~4-"^"..a "n " _.b. b n e (u) n_.u. a.: 4. s i n n e t A.. C _ s-

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.i.n. s.u a. A s ~we a~.a, .- a z -. s. s --o --v _n.-. u. a. c o o.3 a..+- .a.n.c a.m..oopu.a_.en. e: u.u. e n n n.. ; .-..e.m. u. u--..A_;, u. n, a u. a..A ( 3 )' ~.u. e c - a ; n.i. a.. 2.3. r. ;.. ,v, :.. u. a. n..u.e e n a.1

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.a a-- v. -a_ac o-d"-.i..- H.4-e i-d. ~. ".. e.'...# ^.... a,. 4 o.. ". a..- s i.. - ". v a a u a y - a w m"mb4o s 4- -_=.-~a_-, _4 _ aw. .#.- m.- n_ # s_ - =_.. c a s 1 2.'. d_ 9 I183 Di2

,a Our o.urcoses herein are as follows: (1) to assess the extent of core damage indicated by these three sources of 4,: -...o.ma _nn anu (a) .o cn,s.ia - _ _= :,,. u. a, -.u.,..3 c m . u.e e -u me_ -a- ~, m. c0.e v-nu,a -asu,u ;- ; - sac o..; n, u.. - _a -,, .,,ca .~n - a, ..n., -a _-a ~~ v-- i 4' e - u" - -.i a - 4 " ~ a u" u' ^- 1 a = - ^ h = i.n.- = a ^ - 4 0.".. u3 v Th.. L,nl,Rc, 0 D e,, e,, -. r u c When the reactor coolant "umo.s in the A loco were shut e

  1. ~

Acwn '0.1 .m u".es =-_s-

  • ".o.

s*-=.- c# ".". e = " ^- 4 A = a -, " o.i l.d.".y~ r 4-1 s. u this 1000 had alreadv. been under wav. for some time, and there was a considerable void (steam) volume in the loop. N.h4'a

  • k.e" con-i."adn -

". o - "a."., *he "eu ~- "es, -. = d u 4 " 4 ^ ". "' i" - A circulating aater and steam throughout the loop, also a;ted as a hemogeni:er of the water-steam mixture. In this way water continaed to flow through the reactor, to kee.o the fuel rods wet, and thereb" to keep those rods cool. When the 3-1oo0 oumos were turned off at 73 minutes, chase separation took place within that loop. The water present in the primary side of the B steam generator settled to the bottom of that steam generator, and th steam rose to the too. That water was trac.ced there in t..e bottom of the steam generator and unable to flow into the reactor because of the low el.evation of the steam cenerator relative to the reactor. The reactor-ccolant ausps in the A loop continued to e circulate water and steam through both the reactor and the A steam generator until these pumps were also turned off at 30.3 m.4..,, os me or a a. ou:.w - a -4ae... n o.a. - o n m-o 3 -..o a. (p. TH56) estimates 30 percent void (steam) in the reactor and "".e n' a"aa.. 3-m"a =~.o a*-

  • b. a *m t.4.. a..

.# ""e vo.A ~n 4 e - -

  • 4 c.n

-.5.-^ u ~ 5o " " mu" e a' was

  • h = *
b. i ~.".,

a.a.##. .-=v4cw um-- v 3 . woo. incicates that the sucsect'ent thermal history shows that the void fraction in the reactor itself was not that high; perhaps duriny~ their coastdown, the A-lcop coolant pumps continued to pump water and steam into the reactor at a cradually diminishin~m rate, and chase separation within the reactor vessel covered 75-100 percent of the core with water. At this c.oint no heat was beinc. extracted throuc.h the a h h a 3 ). .N -sua, OEN -.N. u h M O--.Oww- .E-- - ---. --<h .1 .u-as a--411 "e.n *- i.". ~; .#.' ". i d - r. - =.4."..~..e ". -. ".' 3.". - - e d a ".- o. ^ ~m f. a inieCtiCn (HPI) from the Emergency Core Cooling 5' stem had / s a.l o " a c r. "..h.- n * - ' e d... '..". e #"al -^da-N. a - =- --^hab'v aa a 0.m..e g w 3 =. o.w n.

e..l o s g kg Z ' E O.7,. ". O s a '*'. '. 4 ".".

-n~a"e.a"'l ^# 6

  • s y.

~ . u. o hg-. 4."..e. To.l'owi"~ ~* - - + 3 *v .w - -.' ~..e, .h. a. d o a ';' ". "- =. o ne. w u; -a-- .J.w e g.. .". e " o.. d o.". o # ..". e

  1. "al
  • ^ds "e'^w

..".o. - - g "a - - oU"#'F^ ' i~ i# ~ y a.' w e.". ~.i.n t o k o 4 1 ".".3~ w= e. 3 e c.= "a a e '.". i ' a '.' "; ~ ". a. c^v o waa-

m. a 2.*.1y

- Q y a.w a a. eg A ".k u _2. 9.9, $ } n.e - a .A.w 3 A. ". 4 m. Q. . %. a. " men.' ~ = vi -s-- - i 1183 313

4 d a ^ a " ". e =. '. ".. a..". m _.i ".~, -a y na.= ad " c _i _' a_ d 'a' ~ a - m..4 o.-^u" cod 4 -a =- o n _ a....

2. a-4..a v. o. e c r. =.4

.k. a "o'_'ad = '4 a v,, --a -, '4 = a_.- - -,- - m n.4. e, ;. o- _,.3 _i n c., v-4,. . a. m. ..m,_ 2-- u.e 4,w. ,c

--=.-o g...

n-- ~- ove-ma bv wa a-

m..d,

c - - - i.. ~:.' *;, -d .' a = s v. a -.-

  • o a s " "- i _' a_ d.

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  1. =

=- - -.i..' v..- a o.. d i v vyy-- .".e be,.i.n i.. ~# -"i-. "..e....=.1 a '..' u= ".., bu. ~5.e -= a o# u -u-o fall slowed as less and less of the fuel-rod length was covered by water. Ir turn, the rate of steam evolution was also high at ww -..e ow--v of n.4 s e h o ~..., l._ a.._=.4 e n., w,,. l2 s- -a _i n o-

0_m2,

,v+ 3 t o-u a m s g no a ad-- ac. b.e 'n a " a - 'a"a' cou--"-"ed ~3 - =.'.' ""e 'a'a a- ~a. s t a a ~.. _#.' ^ w.i - ~ "y a s ".

  • ..".e

'y,-ca." "7o - _ _4 " ". ^# .". e .# ". a '__. da s' ^'

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o n--- ^^ u ti.ese - ds a.4 'v.".a-ab"y _.".e s-e =.~... a.. "ee a * "-' = 'a u' s a _' s e d. ..".e o - a s e.".c e C. "..h..i s s " ^ye..h.ea ad a o =.~. 'n n - 4.. d.i ~- n ' d k" a ~; rising not-leg temperatues at the reactor outlet. As time wore on and the water level in che reactor fell, less steam was available to cool the upper portion of the fuel rods, but more cooling was needed because a greater lenc :h of fuel rod was exposed to the steam. The results were that the t o.... ee.-a.u.-a c# +5a-. a y^ e..- yo-*-- n o#. -he i- - e. .-^do-a--; 4 4' rose rather slowlv., but the temperatue rose more and more rapidly as progressively less steam was available for ooling an increasing fraction c fuel-rod length. Rupture of the Fuel Rods As the fuel-rod temperatures rose, the 'elium with w"u. - b .".e . od s.had b a a.n #.4.1.1 ad-c' u..4..^3 .b.e _i _- ..m= u u." ' c "-.- e a.' 0 o i a rose in pressure. With the rising temocratures, the strength of the fuel's irconium cladding declined, and t ".a - e # o.- o 4 s abi.li_v, o .-esi-* *".e __i .4..~ .'.n e o_.-.. =.? ~'s a. a 3 pressure diminished fairly rapidly. Because the circonium had not yet been oxidized to a significant extent, the claddin~ was very ductile and therefore bul ed ander the w conditions of rising internal pressure and falling clad s .-o. s.g. -S.is bulgi..3~ "aas e.~^"ak.iv 3.-a = e s - 4.. b.e u c_,c a.- ~ e m .u portion of the core whe-a #"el-red temperatures were high and clad strenc.th low. When rod temo.erature eached about 1500 F, the rods split probably in their hottest, uc.cer cortions, releasinc to the reactor coolant both the helium w.'..". w"...'*5 ".a_.ods' h.a "ea.m .#.'.'.' a_ d =..d d

=~er"a

. ' c s.' o r. ~ d --- u -. v^ d u ^ - s- /,s u " 5 = s- .v.e r.v u...c' >... v, ".s..i . ". a. ". = w a_ s v^ y= - a. d-__-^.a y ^- ^ d 3 .w ... e a v,.7 4 a .n.e. ..a .4X 4 n o ne.. e 7 ...m

,c1

,g.

s ayaCa.
2. _1

.w. -a " G a C "i - -. a..*.."y e. 3 "-.- o_ s a " C *I a. d .l'00 7 a u" d..h a - ^ # ^ - a_ ^ - ^ ^ a '^ _' ; =.l ' 3 v. y&- .uc --ad -.5.'a-wa";. ~. 5 e ,.a...a -. ".. "n...i .h. "..'a-u"=.' k .' a c u.4.. ~ -..d -"c*"-= ^_^u.'a ". a-. a. ^ u~ ^ "-..- a. d da= m 4 'ad a - - -....- a..' s - a.. c a. a o - - - - .w w w.-. .r... A 4.. _.:.1 7 o -.a,

1.. 3 ' _i, -. e :.. e.1

- d s. m,,.,,_ L.a.. j v

_a Release of these gaseous ficaion products to the reactor coolant probabl'; began shortly before the PORV was closed. During the period 134-180 minutes from start of the accident, the following alarms gave indication of the release of these fission products: the particulate channel, gas-channel and iodine-channel radiation monitors in the containment building; in that interval, the count rates on these channels all increased and went off scale high. OXIDATION OF THE ::IRCONIDI CLAD As temperatures continued to rise in the upper portion of the core, the circonium cladding began to oxidice, embrittling the clad. This oxidation also p-aduced heat that resulted i:. more rapid temperature rise for the fuel and in accelerated oxidation. The Cathcart-Pawel relation for oxidation of the circonium is giver. by the fcllowing (ref. 12). dr =.01126 exo (-33890) (1) d ~- i _,. a n 7.,> O 5 \\ s where oxidized thickness, cm t time, s T temperature, K The rate of oxidation at any given moment was thus dependent not on temperature alone but also on the amount of oxidation

that ad already taken place.

Roughly, the oxidation rate was such that at 2000'? the heat release from clad cxidation equaled the decay heat. As reference 11 describes, zirconium tubing retains a fair amount of its strength if its local cxidation is less than 10 percent, but it becomes very brittle if the oxidation is 13 percent or greater. Although embrittlement by the hydrogen generated is a potential concern, reference 11 also points out that embrittlement of the clad by oxidation is the more severe problem. Reference 1 constructs an inventory of the ".ydrogen generated and from this infers that from 44-63 percent of all the zirconium in the core was oxidized. Because oxidation penceeded most rapidly where temperature was high (eg. 1), tne oxidation was concentrated in the apper par: cf the core. The portion of the fuel rods that was continually immersed in water (perhaps the bottom 20-30 percent) was kept cool by that water and thus did not oxidi:e. Above the lowest water level, the oxid='_cr is graded from sl_;ht i183 015

6 to moderate to heavv. Inasmuch as even 13 cercent oxidation .r o d '.ic a s a = ". e - a a..b 4 - *.T a....a.7 - /.- a #. -->'1', = o. .v.-.aa--- ." e ^ i a' e upper 60-70 percent of the fuel rods was severely embrittled and "aas l '.'< e ' " ' o s - " ". s o-" ...-"----.a 4-a, 4-". a-- r i.a. d.4.7 y - a' *2-m^v~ e.". i.. / e....-";

  • d

-..d i = ". a d i ""=-...-,, o'3s' o." a m v zirconium in the reactor has been oxid :ed. The upper 60-70% of the circorium clad is so embrittled that it has lost its structural inteeritv. The upper perhaps 30-40 percent of the core had its ,4.-e 4 p.- m o.,,0.m.,u o x.: c _4,m a, aua

w. 4

,-,s _ a =- s~ =- cluo 4 .y -.. 2 . = e.- c o n c a. -.i..~, .".a. "a.m:a = "-as a-a.4..ed. 7 - e m a," a *- " '.". (' ) a the complete oxidation of the 26.5-mi.' zirconium clad requires at least 40 minutes at 3000'F or above ar, at leas: 12 minutes at 3500'F or above. These temperatures and times are, of course, required at the lower boundar2 of the zone of complete oxidation; higher temperatures and longer times would have prevailed within.his zone of complete oxidation. ar r,sr. O.e r se rOxJ m.enDLCm.e --u~n .i av The fission products released from the fuel also provide information on the extent of fuel damage and on the -aak *a..ee.a "--as -a_ = c.he d. 7 n ",a.n.e..a 1, 'n i - " __a_- "" 1 y-temperatures produce greater releases of fission products than low, expressed as proportions of the quantities of each -iven isotooe.croc.ucec in tn.e :1ssioninc. c.rocess. at nien s fuel temperatures (above 3500 F), comparable croportions of 21ssion gases (such as xenon) enc volatile tission procucts (such as iodine and cesium) are released by reactor fuels. However, the chemically active species (such as iodine and cesium) are more readily trapped by adsorption on surfaces or as preciptates, such as silver iodide. For this reason tne :1ssion c.ases are simo,er to trace and mo-a -a, lac,e. Herein the.v will be relied on exclusivelv.; attention will focus on Xe-133. Of the xenon produced by fissioning, 57 percent (refs. 1 and 13) to 60 percent (ref. 14) was released from the fuel. Loren: (ref. 15 shows how the proportion of fission gas release depends on fuel temperature and time a: ."aa o.. e = -.-a. e.1'oda-o.# = .'m..,- .".c u - e, ~, = -. - ". - -...' a. ^3 ~'- w.a. 4--4-, ,,s w.ould "a -='a=aed "v.

  1. "el

- ". = - 44A -aa--.. e..x c a a d o'00*"- ( _' 9 0 0 ' r ). D u. 4.. ~3 ..". e *-.k. a - a = 1 .. =.. a d a.n.. _. v-a .'O' O .m..i"u a-a.". a.- U. ".i.. a_...', = : o *u *4^- r# ..".a. ^^ra a u y .-so s. v. 'r a.*".ays ^0 'a: e -or*) .- a... = -.. a d oo ^-u14 ". ". 3 -.". - =..i o = a~ e d- -a- ^ + va-", .'.'.. i a.- 3 4

  1. . 4. s.4 a n,=..

~7 ."-.7.. .". a-,o-.--.

  1. ..h a.

^ '^^ ^ .E.d e - w m c' o-Aeo Su ogre 6..%.a. E E a n-4.va - - - - - - - s L' *:* -vo a.5 'm s e ~..%. a

  • y as o T

e sa w. a.p .n is p mm c n w a - 2 2.3. .wacuc od, cg : g.en' - y s.' i ]. to. .J"el -A a an / ,s en- - -.e.c:..g - - a.#.. a f - u ld v o - a.. ".". '4--'a ^3 34-- -'--d - s o.' '+.. :=cas asv ,-c- -= e,-.. a. ". a..- v, -.o c, .o., 1183 016

I .c a _' a a s e o.# a73 o# ". k..e ^ - = _' ~ -.."a.n o.-; "v _# v. o... _#.-.. '.,/.7 4- '"e

  1. "s'

-a o"* c."- -.- o s a n v2, - a..' e = a e

  1. .-^~. *",=_

.-'.o.. ^# y no .cual. ..- - - _ - -.. ~,.o weem.e m.. - m

wa4,

- _ e. c..-mw2 -wm n: .-m y------- order of 2430-2500 C (4350-4500'F) would be recuired ".h ou~.". yo.-*_4cn. ^# . ". a. -o. a s. w. Res: in attachment 4 to reference 6 shows that the proportion o- *'ssion gases released is sensitive to se" era. factors. One of these is ~ rain bo"rdary separation. If the w c l w2 - e -. s a c.-a=".-- den' ^# .#. a c

  • u - 4..c.

a.' o r.~:. ". e - = 4. o 3_ b o "-..A a ' a s, -"e

  1. 4 s4on

~,s -a'a_==e _4 -a s"" s a..-=.'.i " "4 -".o_ - .-y. u -u __a .".a n _' _= - u" a ~~=4.. b o u..A a.. 4 a s d.' A .n.o " s = y _=

m. - -.

'..'s.'.'. -.". o -^. a J. u a_ _l -"*bab'"y "..4~'3'V _# " _' " ~.a.. a d # _- ^ ~.. ""a o "m ". - ^ o _ " ", o. ~ ~ _s y.- 3., yn -u-

  • h. o. w.. 2 7-

- ;.~ 7 a - . b.._w o n g.h. 4p. i -w 4*.,3ma;cA, o.v.y e c ; - _1 ',

q. w.e n.

2 w. .--o v.. 4 .A -..~..u,--_A 4.,. +w o s.u. a. yo. vgwa,. t" v, u. a n. t.-==, 1-), _4,.. yg g.w .., o-w u .ca w- .J 1 a particular, conc.yumes t,na t a portion or_ t, e :' e 3 is :1ne3y n divided. Rest also states that fuel power dsnsity (kW'f:) / a # #eC*o~ -"e sxo. "..#

  1. Uel 1 3 *- 4 C e N. "..i ~ "

e e a s e w i t.",a s ". " b b l a s.i.". ".h.a -a arrects tn. . n wnicn the gases can escapa from t.s.e fuel lattice. Because the release of fiss on gases depends on so '..v ui.k".ow.. a - d "-.".c ^.. _ o '.' e d .# _'""o- "'F. ', " ". = -u o .cuel "a.y..a u-as o# ,'3~0-4a~Cv~ r a .". -o u y~ k o u"- - ". e e y _.- ','3 o# -. a -a

  • "s e u~ o.- o a-a ".n.',v a ou~h.

.i-di a"_icn o# "'.a - a..,a_. = " "- - o y a ac tua1 ' '1j achieved. Findincs:- (1 ) .w.e re1 ease or t e gaseous 21ssion procuCO Xenon n ,w - e.i -.n d '. "a*as "".a_ e..".ayo- * ". a - - e _9,' 3 ^-.# " ". e ..on -.- m y

u. -

-yy Cewo a.v - a a A 2 A,u003D. '^ ( s- ) C n,+, n u,.4.,.g-4 c.u. n,, c.= c.o---- a ,,4 --A c, r, c -a Ba into the reactor's cooling water indicates that some of the rue:, 1s in :1 rely c..ivi,e, form.

e. d. e R,,a,u.

- - --n o.1 0 :- a n.. - C azor-. ". ".e '. "..e -...a.l - h'] d a u ' i - = n = ' v s.4 o.#

  • ".. a -- _- a. b":

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