{"id":18268,"date":"2018-07-15T15:32:10","date_gmt":"2018-07-15T15:32:10","guid":{"rendered":"http:\/\/sitepourvtc.com\/?page_id=18268"},"modified":"2023-01-28T13:56:14","modified_gmt":"2023-01-28T13:56:14","slug":"inverse-reactor-kinetics-reactimeter","status":"publish","type":"page","link":"https:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/reactor-dynamics\/inverse-reactor-kinetics-reactimeter\/","title":{"rendered":"Inverse Reactor Kinetics &#8211; Reactimeter"},"content":{"rendered":"<div   id="8n9s8rpp6h"    class=\"su-quote su-quote-style-default\"><div   id="8n9s8rpp6h"    class=\"su-quote-inner su-u-clearfix su-u-trim\">The <strong>inverse kinetics method<\/strong> is a reactivity measurement based on the point reactor kinetics equations. The reactimeter is a device (or rather a <strong>computational algorithm<\/strong>) that can continuously give real-time reactivity using the <strong>inverse kinetics method<\/strong>.<\/div><\/div>\n<p>The reactivity describes the measure of a <strong>reactor\u2019s relative departure from criticality<\/strong>. It is important to monitor the system\u2019s reactivity during reactor operation and reactor startup. It must be noted <strong>reactivity<\/strong> is not directly measurable, and therefore most power reactors procedures do not refer to it, and most technical specifications do not limit it. Instead, they specify a limiting rate of neutron power rise (measured by excore detectors), commonly called a <strong>startup rate<\/strong> (especially in the case of <a href=\"http:\/\/sitepourvtc.com\/pwr-pressurized-water-reactor\/\">PWRs<\/a>).<\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/06\/Reactor-Kinetics-change-in-reactivity-min.png\"><img loading=\"lazy\" class=\"size-medium wp-image-18124 alignright\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/06\/Reactor-Kinetics-change-in-reactivity-min-300x216.png\" alt=\"Reactor Kinetics - change in reactivity\" width=\"300\" height=\"216\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/06\/Reactor-Kinetics-change-in-reactivity-min-300x216.png 300w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/06\/Reactor-Kinetics-change-in-reactivity-min.png 825w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/a>On the other hand, during reload startup physics tests performed at the startup after refueling the commercial PWRs, it is important to monitor subcriticality continuously during the criticality approach. On-line reactivity measurements are based on the inverse kinetics method, and the inverse kinetics method is a reactivity measurement based on the point reactor kinetics equations. This method can be used for:<\/p>\n<ul>\n<li><strong>Reactivity measurement at high neutron level<\/strong> &#8211; <strong>reactimeter without source term<\/strong>. A reactimeter can be constructed without source term, but it works only at higher neutron levels, where the neutron source term in point reactor kinetics equations may be neglected.<\/li>\n<li><strong>Reactivity measurement at subcritical multiplication<\/strong> &#8211; <strong>reactimeter with source term<\/strong>. For operation at low power levels or in the sub-critical domain (e.g., during criticality approach), the contribution of the neutron source must be taken into account, and this implies the knowledge of a quantity proportional to the source strength and then it should be determined. The subcritical reactimeter is based on the determination of the <strong>source term<\/strong> (source strength).<\/li>\n<\/ul>\n<p>As was written, the system\u2019s reactivity can be measured by a <strong>reactimeter<\/strong>. The reactimeter is a device (or rather a <strong>computational algorithm<\/strong>) that can continuously give real-time reactivity using the <strong>inverse kinetics method<\/strong>. The reactimeter usually processes the signal from source range excore neutron detectors and calculates the system\u2019s reactivity.<\/p>\n<p>It was shown that the source term is not easy to determine, and the problem is that it is of the highest importance in the subcritical domain. One recognized method for source term determining is known as Least Squares Inverse Kinetics Method (<strong>LSIKM<\/strong>).<\/p>\n<p>Special reference: Seiji TAMURA, \u201cSignal Fluctuation and Neutron Source in Inverse Kinetics Method for Reactivity Measurement in the Sub-critical Domain,\u201d J. Nucl. Sci. Technol, Vol.40, No. 3, p. 153\u2013157 (March 2003)<\/p>\n<h2>Inverse Kinetics &#8211; Equations<\/h2>\n<p>The <strong>exact point kinetics equations<\/strong>\u00a0that can be derived from the general neutron balance equations without making any approximations are:<\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/07\/Reactor-Kinetics-source-term.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-18208\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/07\/Reactor-Kinetics-source-term.png\" alt=\"Reactor Kinetics - source term\" width=\"313\" height=\"166\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/07\/Reactor-Kinetics-source-term.png 313w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/07\/Reactor-Kinetics-source-term-300x159.png 300w\" sizes=\"(max-width: 313px) 100vw, 313px\" \/><\/a><\/p>\n<p>where:<\/p>\n<ul>\n<li>n(t) is the neutron density in the core (which is proportional to the detector count rate)<\/li>\n<li>C<sub>i<\/sub>(t) is the precursor\u2019s density of delayed neutrons of group i<\/li>\n<li>\u039b is the prompt generation time<\/li>\n<li>\u03c1 is the reactivity<\/li>\n<li>the constants \u03b2<sub>i<\/sub> and \u03bb<sub>i<\/sub> are the fraction and decay constant of delayed neutron precursor of group i<\/li>\n<li>S(t) is the source term, which characterizes the number of neutrons (<a title=\"Source Neutrons and External Source of Neutrons\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/reactor-dynamics\/subcritical-multiplication\/source-neutrons-and-external-source-of-neutrons\/\">source neutrons<\/a>) added to the system from an external source. As can be seen, the source term does not influence the system\u2019s dynamics since it does not influence the system\u2019s reactivity.<\/li>\n<\/ul>\n<p>According to Seiji TAMURA, the Inverse Kinetics equations (flux \u27f6 reactivity) for discrete-time series data can be derived from the ordinary point kinetics equations (reactivity \u27f6 flux), assuming that the reactor power change for the interval of \u0394t is as n(t)=n<sub>j-1<\/sub>exp(\u03bc<sub>j<\/sub>t), where \u03bc<sub>j<\/sub> = log(n<sub>j<\/sub>\/n<sub>j-1<\/sub>)\/\u0394t:<\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/07\/Inverse-Kinetics-Reactimeter-Equations.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-18209\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/07\/Inverse-Kinetics-Reactimeter-Equations.png\" alt=\"Inverse Kinetics - Reactimeter - Equations\" width=\"346\" height=\"204\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/07\/Inverse-Kinetics-Reactimeter-Equations.png 346w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/07\/Inverse-Kinetics-Reactimeter-Equations-300x177.png 300w\" sizes=\"(max-width: 346px) 100vw, 346px\" \/><\/a><\/p>\n<p>When the reactor power is at a steady-state n<sub>o<\/sub>, seven initial conditions can be obtained as:<\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/07\/Inverse-Kinetics-Reactimeter-Equations_2.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-18210\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/07\/Inverse-Kinetics-Reactimeter-Equations_2.png\" alt=\"Inverse Kinetics - Reactimeter - Equations_2\" width=\"236\" height=\"67\" \/><\/a><\/p>\n<p>The equation for \u03c1<sub>j<\/sub> provides a real-time reactivity calculation for successive reactor power data. When the reactor is operating at a sufficiently high power level, the last term of the right side, the source term, may be neglected because it becomes negligible.<\/p>\n<p>For operation at low power levels or in the sub-critical domain (e.g., during criticality approach), the contribution of the neutron source must be taken into account, and this implies the knowledge of a quantity proportional to the source strength and then it should be determined. Otherwise, zero reactivity will be obtained for any subcritical reactor condition (after the transition phenomena have died out). The source term can be determined using data from a transient state after introducing a given reactivity. The source term can be determined from data from the rod drop experiment using the Least Squares Inverse Kinetics Method (LSIKM).<\/p>\n<p><strong>Special reference:<\/strong> M. Itagaki, A. Kitano, \u201cRevised source strength estimation for inverse neutron kinetics,\u201d Preprints 1999 Fall Mtg., At. Energy Soc. Jpn., Hiroshima, Japan, G20, (1999)<\/p>\n<p><strong>Special reference:<\/strong> Renato Yoichi Ribeiro Kuramoto, Anselmo Ferreira Miranda. SUBCRITICAL REACTIVITY MEASUREMENTS AT ANGRA 1 NUCLEAR POWER PLANT. 2011 International Nuclear Atlantic Conference &#8211; INAC 2011. ISBN: 978-85-99141-04-5.<\/p>\n<div   id="8n9s8rpp6h"     class=\"lgc-column lgc-grid-parent lgc-grid-100 lgc-tablet-grid-100 lgc-mobile-grid-100 lgc-equal-heights \"><div   id="8n9s8rpp6h"     class=\"inside-grid-column\">\u00a0 <div   id="8n9s8rpp6h"    class=\"su-accordion su-u-trim\"><div   id="8n9s8rpp6h"    class=\"su-spoiler su-spoiler-style-default su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\"><div   id="8n9s8rpp6h"    class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>References:<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\"><strong>Nuclear and Reactor Physics:<\/strong>\n<ol>\n<li>J. R. Lamarsh, Introduction to Nuclear Reactor Theory, 2nd ed., Addison-Wesley, Reading,\u00a0MA (1983).<\/li>\n<li>J. R. Lamarsh, A. J. Baratta, Introduction to Nuclear Engineering, 3d ed., Prentice-Hall, 2001, ISBN: 0-201-82498-1.<\/li>\n<li>W. M. Stacey, Nuclear Reactor Physics, John Wiley &amp; Sons, 2001, ISBN: 0- 471-39127-1.<\/li>\n<li>Glasstone, Sesonske. Nuclear Reactor Engineering: Reactor Systems Engineering,\u00a0Springer; 4th edition, 1994, ISBN:\u00a0978-0412985317<\/li>\n<li>W.S.C. Williams. Nuclear and Particle Physics.\u00a0Clarendon Press; 1 edition, 1991, ISBN:\u00a0978-0198520467<\/li>\n<li>G.R.Keepin. Physics of Nuclear Kinetics.\u00a0Addison-Wesley Pub. Co; 1st edition, 1965<\/li>\n<li>Robert Reed Burn, Introduction to Nuclear Reactor Operation, 1988.<\/li>\n<li>U.S. Department of Energy, Nuclear Physics and Reactor Theory.\u00a0DOE Fundamentals Handbook,\u00a0Volume 1 and 2.\u00a0January\u00a01993.<\/li>\n<\/ol>\n<p><strong><\/strong><strong>Advanced Reactor Physics:<\/strong><\/p>\n<ol>\n<li>K. O. Ott, W. A. Bezella, Introductory Nuclear Reactor Statics, American Nuclear Society, Revised edition (1989), 1989, ISBN: 0-894-48033-2.<\/li>\n<li>K. O. Ott, R. J. Neuhold, Introductory Nuclear Reactor Dynamics, American Nuclear Society, 1985, ISBN: 0-894-48029-4.<\/li>\n<li><span style=\"font-weight: 400;\">D. L. Hetrick, Dynamics of Nuclear Reactors, American Nuclear Society, 1993, ISBN: 0-894-48453-2.\u00a0<\/span><\/li>\n<li>E. E. Lewis, W. F. Miller, Computational Methods of Neutron Transport, American Nuclear Society, 1993, ISBN: 0-894-48452-4.<\/li>\n<\/ol>\n<\/div><\/div><\/div><div   id="8n9s8rpp6h"    class=\"su-divider su-divider-style-dotted\" style=\"margin:15px 0;border-width:2px;border-color:#999999\"><\/div><\/div><\/div><div   id="8n9s8rpp6h"    class=\"su-divider su-divider-style-default\" style=\"margin:15px 0;border-width:2px;border-color:#999999\"><\/div><div   id="8n9s8rpp6h"     class=\"lgc-column lgc-grid-parent lgc-grid-33 lgc-tablet-grid-33 lgc-mobile-grid-100 lgc-equal-heights \"><div   id="8n9s8rpp6h"     class=\"inside-grid-column\"><\/div><\/div><div   id="8n9s8rpp6h"     class=\"lgc-column lgc-grid-parent lgc-grid-33 lgc-tablet-grid-33 lgc-mobile-grid-100 lgc-equal-heights \"><div   id="8n9s8rpp6h"     class=\"inside-grid-column\">\n<h2>See above:<\/h2>\n<p>Reactor Dynamics<a href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/reactor-dynamics\/\" class=\"su-button su-button-style-flat\" style=\"color:#606060;background-color:#ffffff;border-color:#cccccc;border-radius:10px;-moz-border-radius:10px;-webkit-border-radius:10px\" target=\"_self\"><span style=\"color:#606060;padding:7px 20px;font-size:16px;line-height:24px;border-color:#ffffff;border-radius:10px;-moz-border-radius:10px;-webkit-border-radius:10px;text-shadow:0px 0px 0px #000000;-moz-text-shadow:0px 0px 0px #000000;-webkit-text-shadow:0px 0px 0px #000000\"><i class=\"sui sui-link\" style=\"font-size:16px;color:#5d5d5d\"><\/i> <\/span><\/a><\/p><\/div><\/div><div   id="8n9s8rpp6h"     class=\"lgc-column lgc-grid-parent lgc-grid-33 lgc-tablet-grid-33 lgc-mobile-grid-100 lgc-equal-heights \"><div   id="8n9s8rpp6h"     class=\"inside-grid-column\"><\/div><\/div>\n","protected":false},"excerpt":{"rendered":"<p>The reactivity describes the measure of a reactor\u2019s relative departure from criticality. It is important to monitor the system\u2019s reactivity during reactor operation and reactor startup. It must be noted reactivity is not directly measurable, and therefore most power reactors procedures do not refer to it, and most technical specifications do not limit it. Instead, &#8230; <a title=\"Inverse Reactor Kinetics &#8211; Reactimeter\" class=\"read-more\" href=\"https:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/reactor-dynamics\/inverse-reactor-kinetics-reactimeter\/\" aria-label=\"More on Inverse Reactor Kinetics &#8211; Reactimeter\">Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":18114,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"generate_page_header":""},"_links":{"self":[{"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/pages\/18268"}],"collection":[{"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/comments?post=18268"}],"version-history":[{"count":3,"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/pages\/18268\/revisions"}],"predecessor-version":[{"id":36984,"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/pages\/18268\/revisions\/36984"}],"up":[{"embeddable":true,"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/pages\/18114"}],"wp:attachment":[{"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/media?parent=18268"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}