NPTL Chemcal ngneerng Nuclear Reactor Technology Moderator & Moderator System K.S. Rajan Professor, School of Chemcal & Botechnology SASTRA Unversty Jont Intatve of IITs and IISc Funded by MHRD Page of 9
NPTL Chemcal ngneerng Nuclear Reactor Technology Table of Contents COMPARISON OF MODRATORS BASD ON MODRATING RATIO... 3. MODRATING RATIO... 6 MODRATOR SYSTM IN PRSSURIZD HAVY WATR RACTOR... 8 3 RFRNCS/ADDITIONAL RADING... 9 Jont Intatve of IITs and IISc Funded by MHRD Page of 9
NPTL Chemcal ngneerng Nuclear Reactor Technology In ths lecture, we shall dscuss the choce of materals as moderators, ther merts and demerts along wth ther mplcaton n the desgn of a nuclear reactor. A bref descrpton of moderator system of PHWR wll also be dscussed At the end of ths module, the learners wll be able to () () () (v) understand the physcs behnd neutron thermalzaton calculate the number of collson requred for thermalzaton calculate moderatng rato and compare moderators based on moderatng rato understand the functonng of moderator system n PHWR Comparson of moderators based on moderatng rato We have seen the use of varous materals as moderators n dfferent nuclear reactors. One may also recall a reactor classfcaton based on the moderator. That leads us to two mportant questons: () what type of materals s sutable as moderator? () What s the method of comparng the performance of dfferent materals used as moderators? To answer the frst queston, we shall recollect dfferent type of nuclear reactons. Durng elastc scatterng, the speed and drecton of a neutron are changed due to elastc collsons wth a nucleus. The neutron looses a part of ts knetc energy and hence slows down. These are the thermal neutrons that help the nuclear chan reacton to sustan. Ths process s called moderaton. The nucleus wth whch the neutrons undergo elastc collson must be conducve for thermalzaton. In other words, the probablty of elastc reacton between neutron and the nucleus must be hgh. In terms of cross sectons, the nuclear cross secton of a moderator s nucleus for elastc scatterng (σ el ) must be hgh. Usng the analogy of collsons of bllard balls for elastc scatterng, t s possble to relate the mass of target or moderator nucleus (M), energy of ncdent neutron ( ) and the energy of scattered neutron ( s ) usng the laws of conservaton of mass and energy, as follows: s M m M + m n n () If the atomc mass of the target or moderator nucleus s approxmated to ts mass number (A) and mass of a neutron as amu, then A A + s () Jont Intatve of IITs and IISc Funded by MHRD Page 3 of 9
NPTL Chemcal ngneerng Nuclear Reactor Technology Note: The smultaneous soluton of momentum and energy conservaton equatons for elastc collson between two bodes (as n the case of collson of a neutron wth a nucleus) gves two solutons: Soluton I: Intal and fnal energes of neutron are same. In ths case, there s no change n the drecton as neutron contnues to travel n forward drecton. Hence s Soluton II: The neutron s scattered at 80.e. the drecton of neutron s completely reversed. The energes of ncdent and scattered neutrons are related by equaton () In realty, the drecton of scatterng may range from 0 to 80. Hence, the average energy of scattered neutron may be taken as the average of energes wth scatterng angle 0 and 80. Therefore, s s A + A + A + A + A + A + A + A + A + The above equaton can be graphcally represented as shown n fgure. (3) (4) From fgure t s clear that lower the value of A, lower s the s / rato. Hence lght nucle are more effectve n moderatng compared to that of heavy nucle. Ths s the ratonale for usng water (hydrogen as scatterng nucleus), heavy water (deuterum as scatterng nucleus) and graphte (carbon as scatterng nucleus). quatons () to (4) gve the rato of knetc energes of scattered and ncdent neutron after one collson. However to thermalze the neutrons by reducng ts energy from few MeV to 0.053 ev (8-orders decrease n knetc energy) the neutron must undergo several successve elastc collsons wth the moderator. The mean logarthmc energy decrement (ξ) defned as ln( / s ) s related to the mass number of moderator as: ξ ( A ) A A + ln A (5) Hgher the value of ξ, more effectve the moderaton s due to the lower energy of scattered neutron compared to the ncdent neutron. quaton (5) can be represented dagrammatcally n Fgure. It s clear from fgure that ξ s hgh for nucle of lower atomc number. Jont Intatve of IITs and IISc Funded by MHRD Page 4 of 9
NPTL Chemcal ngneerng Nuclear Reactor Technology 0.9 0.8 s / 0.7 0.6 0.5 0.4 0 0 0 30 40 50 60 70 80 90 00 Atomc number Fg. Rato of energes of scattered neutrons to ncdent neutrons 0.9 0.8 0.7 0.6 ξ 0.5 0.4 0.3 0. 0. 0 0 0 0 30 40 50 60 70 80 90 00 Atomc number Fg. Mean logarthmc energy decrement as a functon of atomc number If hgh and thermal are the knetc energes of hgh energy neutron and thermal neutron respectvely, then Jont Intatve of IITs and IISc Funded by MHRD Page 5 of 9
NPTL Chemcal ngneerng Nuclear Reactor Technology hgh hgh n thermal.. 3... thermal (6) hgh thermal ξ ξ ξ e. e. e... e ξ e nξ (7) The followng example shows the calculaton of nuclear of collsons for a typcal case xample : Determne the number of collsons requred for thermalzaton for the followng case. Data: nergy of ncdent neutron hgh MeV nergy of thermal neutron thermal 0.053 MeV Moderator: Heavy water ξ 0.509 Soluton: Usng q. (7) e 0.053 e6 0. 509n (8) Solvng q. (8), we get n 34 For lght water (ξ 0.90) and graphte (ξ 0.58) as moderators, the numbers of collsons requred for reducton of neutron energy from MeV to 0.053 ev are 9 and respectvely (calculated usng equaton 7).. Moderatng rato It may be recalled that the nuclear cross sectons represent the probablty of varous nuclear reactons. When neutron nteracts wth a nucleus, one of the followng can happen: elastc scatterng, nelastc scatterng, neutron capture and fsson. As we have seen earler, the slowng down of neutrons s due to the elastc scatterng of neutron by the nucleus of moderator. If the capture cross secton of moderator (σ γ) s hgh, most of the neutrons wll be absorbed by t, leadng to lower moderaton or lower avalablty of thermal neutrons. Hence a hgher rato of scatterng to capture cross sectons (σ el /σ γ) s desrable for effectve moderaton. Combnng ths rato wth mean logarthmc energy decrement Jont Intatve of IITs and IISc Funded by MHRD Page 6 of 9
NPTL Chemcal ngneerng Nuclear Reactor Technology (ξ), moderatng rato can be calculated whch can be used as a crteron for comparson of dfferent moderators. Moderatng rato ξσ el σ γ (9) Moderatng rato wll be hgh f ether of (ξ) or (σ el /σ γ) s hgher. The followng table gves the values of ξ, and σ el /σ γ of some common moderators. Table. Moderatng rato for common moderators. Note that the cross sectons are correspondng to the neutron energy of 0.053 ev (thermal neutron) Moderator ξ σ el (b) σ γ (b) σ el /σ γ Moderatng rato n Lght water 0.90 5.47 0.33 77.7 7 9 Heavy water 0.509 5.57 0.0005 39.49 5670 34 Graphte 0.8 5.5 0.0035 500 9 Though lght water has the hghest ξ and σ el among the three moderators shown, ts moderatng rato s low due to ts relatvely hgher capture cross secton. Heavy water has the hghest moderatng rato owng to ts lowest cross secton for neutron capture. Graphte, despte possessng the lowest ξ and σ el, fars better than lght water due to ts lower σ γ compared to that of lght water. The relatve advantages and dsadvantages of heavy water and lght water, the common moderators n Indan reactors are as follows: Table. Relatve advantages and dsadvantages of lght and heavy water as moderator Moderator Advantages Heavy Hgh moderatng rato and hence water can be used wth natural uranum fuel Lght water Less expensve; Requres a core of relatvely smaller dameter as only 9 collsons are requred for moderaton Dsadvantages More expensve; Requres a core of larger dameter to facltate 34 collsons between a neutron and the moderator Can be used only wth enrched uranum fuel Jont Intatve of IITs and IISc Funded by MHRD Page 7 of 9
NPTL Chemcal ngneerng Nuclear Reactor Technology Moderator System n Pressurzed Heavy Water Reactor Coolant and moderator are not separated n lght water reactors. However, despte usng heavy water as both moderator and coolant, they are housed n separate compartments n a pressurzed heavy water reactor. Heavy water as coolant flows nsde the pressure tubes, whle the calandra s mmersed n the moderator. The moderator s not drectly heated by heat transfer from fuel. Instead, moderator s heated due to the energy lost by neutrons durng ther slow down. The energy of prompt gamma radaton s also deposted n the moderator. It may be recalled that about 5 % of 00 MeV of recoverable energy from fsson s released n the moderator. Hence the moderator needs to be cooled to mantan ts temperature, to prevent vaporzaton. Typcally, the moderator s mantaned between 60 C and 80 C. The moderator system s desgned to mantan the temperature of moderator wthn ths range. A schematc dagram of moderator system wth pumps, valves and heat exchangers s shown n Fgure 3. Fg 3. Moderator system of PHWR (Redrawn from Ref. []) Jont Intatve of IITs and IISc Funded by MHRD Page 8 of 9
NPTL Chemcal ngneerng Nuclear Reactor Technology Calandra has outlets at the bottom for the removal of moderator. The nlets for moderator are provded on the sdes of calandra as shown n Fgure 3. Moderator pumps are used to pump the moderator out from calandra and pass them through heat exchangers. Moderator s cooled n these heat exchangers usng lght water suppled for ths purpose. The flow rate of lght water s controlled dependng upon the temperature of moderator. Two heat exchangers are shown n Fgure 3. ach heat exchanger s provded wth an solaton valve that can be used to dsconnect that partcular heat exchanger from the system, for mantenance. In such cases, one heat exchanger can be used to mantan the temperature of moderator. The presence of check valves n the lne ensure that there s no return flow, n case of falure of moderator pump. 3 References/Addtonal Readng. Davd Bodansky, Nuclear nergy: Prncples, Practces, and Prospects, /e, Sprnger-Verlag, USA, 004 (Chapter 7). https://canteach.candu.org/content%0lbrary/00407.pdf Jont Intatve of IITs and IISc Funded by MHRD Page 9 of 9