{"id":15580,"date":"2017-10-02T14:32:15","date_gmt":"2017-10-02T14:32:15","guid":{"rendered":"http:\/\/sitepourvtc.com\/?page_id=15580"},"modified":"2022-10-31T11:53:31","modified_gmt":"2022-10-31T11:53:31","slug":"reflected-reactor","status":"publish","type":"page","link":"https:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/neutron-diffusion-theory\/reflected-reactor\/","title":{"rendered":"Reflected Reactor"},"content":{"rendered":"<p>In previous chapters <a title=\"Nuclear Fission Chain Reaction\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-fission-chain-reaction\/\">(nuclear chain reaction<\/a>), it was derived that <strong><a title=\"Neutron Leakage\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/neutron-diffusion-theory\/neutron-leakage\/\">leakage of neutrons<\/a><\/strong> from the system significantly influences the <a title=\"Reactor Criticality\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-fission-chain-reaction\/reactor-criticality\/\"><strong>criticality of a reactor<\/strong><\/a>. For thermal reactors, two variables are defined to describe the leakage process:<\/p>\n<ul>\n<li><a title=\"Fast Non-leakage Probability\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-fission-chain-reaction\/fast-non-leakage-probability\/\"><strong>fast non-leakage probability<\/strong><\/a><\/li>\n<li><a title=\"Thermal Non-leakage Probability\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-fission-chain-reaction\/thermal-non-leakage-probability\/\"><strong>thermal non-leakage probability<\/strong><\/a><\/li>\n<\/ul>\n<p><strong>The fast non-leakage probability<\/strong> (P<sub>f<\/sub>) and <strong>the thermal non-leakage probability<\/strong> (P<sub>t<\/sub>) may be combined into one term that gives the fraction of <strong>all neutrons<\/strong> that do not leak out of the reactor core. This term is called<strong> the total non-leakage probability <\/strong>and is given the symbol P<sub>NL<\/sub>.\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>Total Non-leakage Probability<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\"><a title=\"Fast Non-leakage Probability\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-fission-chain-reaction\/fast-non-leakage-probability\/\"><strong>The fast non-leakage probability<\/strong><\/a> (P<sub>f<\/sub>) and <a title=\"Thermal Non-leakage Probability\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-fission-chain-reaction\/thermal-non-leakage-probability\/\"><strong>the thermal non-leakage probability<\/strong><\/a> (P<sub>t<\/sub>) may be combined into one term that gives the fraction of <strong>all neutrons<\/strong> that do not leak out of the reactor core. This term is called<strong> the total non-leakage probability <\/strong>and is given the symbol P<sub>NL<\/sub>, and may be expressed by the following equation:<\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/02\/fast-non-leakage-probability_3.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-13679\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/02\/fast-non-leakage-probability_3.png\" alt=\"fast non-leakage probability_3\" width=\"264\" height=\"117\" \/><\/a><\/p>\n<p>We can rewrite this equation without a substantial loss of accuracy <strong>for large reactors<\/strong> simply by replacing the <a title=\"Diffusion Length\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/neutron-diffusion-theory\/diffusion-length\/\"><strong>diffusion length L<sub>d<\/sub><\/strong><\/a> and the fermi age\u00a0<strong>\u03c4<\/strong> with the <strong>migration length M<\/strong> in the one group equation. The term <strong>B<\/strong><strong><sup>4<\/sup><\/strong> is very small for large reactors, and therefore it can be neglected. We may then write.<\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/02\/fast-non-leakage-probability_4.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-13678\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/02\/fast-non-leakage-probability_4.png\" alt=\"fast non-leakage probability_4\" width=\"135\" height=\"173\" \/><\/a><\/p>\n<p>where M is the <a title=\"Migration Length \u2013 Migration Area\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/neutron-diffusion-theory\/migration-length-migration-area\/\"><strong>migration area (m<\/strong><strong><sup>2<\/sup><\/strong><\/a><strong><a title=\"Migration Length \u2013 Migration Area\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/neutron-diffusion-theory\/migration-length-migration-area\/\">)<\/a><\/strong>, the migration length is defined as the square root of the migration area. As can be seen, the total non-leakage probability of large reactors is primarily a function of the migration area.<\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/02\/Neutron-Moderators-Parameters.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-13684\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/02\/Neutron-Moderators-Parameters.png\" alt=\"Neutron Moderators - Parameters\" width=\"666\" height=\"510\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/02\/Neutron-Moderators-Parameters.png 666w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/02\/Neutron-Moderators-Parameters-300x230.png 300w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/02\/Neutron-Moderators-Parameters-180x138.png 180w\" sizes=\"(max-width: 666px) 100vw, 666px\" \/><\/a><\/div><\/div><\/div><div   id="8n9s8rpp6h"    class=\"su-divider su-divider-style-dotted\" style=\"margin:15px 0;border-width:2px;border-color:#999999\"><\/div>Except research reactors, practically <strong>all power reactor cores<\/strong> are designed to minimize the <a title=\"Neutron Leakage\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/neutron-diffusion-theory\/neutron-leakage\/\">neutron leakage<\/a>. <strong><a title=\"Neutron Reflector\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-reactor\/neutron-reflector\/\">Neutron reflectors <\/a><\/strong>surround <a title=\"Reactor Core\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-reactor-core\/\">reactor cores<\/a> to minimize leakage. The neutron reflector scatters back (or reflects) into the core many neutrons that would otherwise escape. By reducing neutron leakage, the reflector increases <strong>k<sub>eff<\/sub> <\/strong>and reduces the amount of fuel necessary to maintain the <strong>reactor critical<\/strong> for a long period.<\/p>\n<figure id=\"attachment_15416\" aria-describedby=\"caption-attachment-15416\" style=\"width: 233px\" class=\"wp-caption aligncenter\"><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/09\/Neutron-Reflector-min.png\"><img loading=\"lazy\" class=\" wp-image-15416\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/09\/Neutron-Reflector-min-345x1024.png\" alt=\"Neutron Reflector\" width=\"243\" height=\"721\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/09\/Neutron-Reflector-min-345x1024.png 345w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/09\/Neutron-Reflector-min-101x300.png 101w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/09\/Neutron-Reflector-min.png 544w\" sizes=\"(max-width: 243px) 100vw, 243px\" \/><\/a><figcaption id=\"caption-attachment-15416\" class=\"wp-caption-text\">Neutron reflector inside a reactor core of LWR. It is only an illustrative example.<\/figcaption><\/figure>\n<p>&nbsp;<\/p>\n<p>In <a title=\"LWR \u2013 Light Water Reactor\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/reactor-types\/lwr-light-water-reactor\/\">LWRs<\/a>, the neutron reflector is installed for the following purposes:<\/p>\n<ul>\n<li>The<a title=\"Neutron Flux Density \u2013 Neutron Intensity\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-engineering-fundamentals\/neutron-nuclear-reactions\/neutron-flux-neutron-intensity\/\"> neutron flux<\/a> distribution is &#8220;<strong>flattened<\/strong>&#8220;, i.e., the ratio of the average flux to the maximum flux is increased. Therefore reflectors <strong>reduce the non-uniformity<\/strong> of the power distribution.<\/li>\n<li>Because of the higher flux at the edge of the core, there is much <strong>better utilization<\/strong> in the peripheral fuel assemblies. In the outer regions of the core, this fuel now contributes much more to the total power production.<\/li>\n<li>The neutron reflector scatters back (or reflects) into the core many neutrons that would otherwise escape. The neutrons reflected into the core are available for a <a title=\"Nuclear Fission Chain Reaction\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-fission-chain-reaction\/\">chain reaction<\/a>. This means that the <strong>minimum critical size<\/strong> of the reactor is reduced. Alternatively, if the core size is maintained, the reflector makes additional <a title=\"Reactivity\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-fission-chain-reaction\/reactivity\/\">reactivity<\/a> available for higher fuel burnup. The decrease in the critical size of the core required is known as <strong>reflector savings<\/strong>.<\/li>\n<li>Neutron reflectors reduce neutron leakage, i.e., to reduce the neutron fluence on a reactor pressure vessel.<\/li>\n<li>Neutron reflectors reduce a coolant flow bypass of a core.<\/li>\n<li>Neutron reflectors serve as a thermal and radiation shield of a reactor core.<\/li>\n<\/ul>\n<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>Albedo - Reflection Coefficient<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\">See also: <a title=\"Albedo Boundary Condition\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/neutron-diffusion-theory\/albedo-boundary-condition\/\">Albedo Boundary Condition<\/a><\/p>\n<p>The reflector&#8217;s efficiency is measured by the ratio of the number of neutrons reflected into the reactor to the number entering the reflector. This ratio is called the <a title=\"Albedo Boundary Condition\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/neutron-diffusion-theory\/albedo-boundary-condition\/\"><strong>albedo<\/strong><\/a>\u00a0or the <strong>reflection coefficient<\/strong>. The albedo can be expressed in terms of <a href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/neutron-diffusion-theory\/neutron-current-density\/\"><strong>neutron currents<\/strong><\/a> as:<\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/08\/albedo-reflection-coefficient-equation.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-15255\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/08\/albedo-reflection-coefficient-equation.png\" alt=\"albedo - reflection coefficient - equation\" width=\"164\" height=\"66\" \/><\/a><\/p>\n<p>The value of the albedo will depend on the<strong> composition<\/strong> and <strong>thickness<\/strong> of the reflector. An infinite reflector will have the maximum albedo. Still, in all practical cases, the geometry of a reflector must conform to the geometry of a <a title=\"Reactor Core\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-reactor-core\/\"><strong>reactor core<\/strong><\/a> and a <a title=\"Reactor Pressure Vessel\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-reactor\/reactor-pressure-vessel\/\"><strong>reactor pressure vessel<\/strong><\/a>. For sufficiently thick reflectors, it can be derived that albedo becomes:<\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/08\/albedo-reflection-coefficient-equation2.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-15256\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/08\/albedo-reflection-coefficient-equation2.png\" alt=\"albedo - reflection coefficient - equation2\" width=\"173\" height=\"56\" \/><\/a><\/p>\n<p>where <strong>D<\/strong><strong><sub>refl<\/sub><\/strong> is the <a href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/neutron-diffusion-theory\/diffusion-coefficient\/\"><strong>diffusion coefficient <\/strong><\/a>in the reflector, and the <strong>L<\/strong><strong><sub>refl<\/sub><\/strong> is the <b>reflection&#8217;s diffusion length<\/b>.<\/div><\/div><\/div><div   id="8n9s8rpp6h"    class=\"su-divider su-divider-style-dotted\" style=\"margin:15px 0;border-width:2px;border-color:#999999\"><\/div><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/10\/axial-and-radial-reflector.png\"><img loading=\"lazy\" class=\"alignright size-full wp-image-15581\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/10\/axial-and-radial-reflector.png\" alt=\"axial-and-radial-reflector\" width=\"286\" height=\"155\" \/><\/a>In general, <strong>neutron reflector<\/strong> may be <strong>axial<\/strong> and <strong>radial<\/strong>, but, for example, in <a title=\"PWR \u2013 Pressurized water reactor\" href=\"http:\/\/sitepourvtc.com\/pwr-pressurized-water-reactor\/\">pressurized water reactors <\/a>the axial reflector does not form any special device. The neutrons are reflected by the core inlet and outlet coolant. On the other hand, common water volume cannot be used as a reflector in the radial direction because it is of the highest importance to maintain high flow rates in the core and not bypass fuel assemblies. Therefore the <strong>radial neutron reflectors<\/strong> are installed in PWR and BWR reactor cores. The design of such radial neutron reflectors may vary, but we can distinguish between two basic types:<\/p>\n<ul>\n<li><a title=\"Core Baffle\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-reactor\/neutron-reflector\/core-baffle\/\"><strong>Core Baffle<\/strong><\/a><\/li>\n<li><a title=\"Heavy Reflector\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-reactor\/neutron-reflector\/heavy-reflector\/\"><strong>Heavy Reflector<\/strong><\/a><\/li>\n<\/ul>\n<div   id="8n9s8rpp6h"    class=\"collapsible-container\">\n<h2>Flux in a Reflected Thermal Reactor &#8211; One-group Method<\/h2>\n<p>The mathematical treatment of a<strong> reflected thermal reactor<\/strong> can be illustrated most simply by considering a <a title=\"Diffusion Equation \u2013 Infinite Slab Reactor\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/neutron-diffusion-theory\/infinite-slab-reactor\/\"><strong>slab reactor<\/strong> <\/a>of thickness extending from<strong> x= -a\/2<\/strong> to <strong>x= +a\/2<\/strong> reflected on both sides by a non-multiplying slab (<strong>neutron reflector<\/strong>) of thickness <strong>b<\/strong>. Neutrons will be considered as monoenergetic with <a title=\"Thermal Neutron\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/atomic-nuclear-physics\/fundamental-particles\/neutron\/thermal-neutron\/\">thermal energy<\/a>. Although the one-group method may provide reasonable results for the reactor, this method does not accurately predict the flux.<\/p>\n<p>For the determination of the<strong> flux distribution<\/strong> in the reactor and the reflector, the following <a title=\"Diffusion Equation\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/neutron-diffusion-theory\/diffusion-equation\/\"><strong>diffusion equations<\/strong><\/a> in these zones need to be solved:<\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/10\/reflected-reactor-equations.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-15582\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/10\/reflected-reactor-equations.png\" alt=\"reflected-reactor-equations\" width=\"596\" height=\"125\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/10\/reflected-reactor-equations.png 596w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/10\/reflected-reactor-equations-300x63.png 300w\" sizes=\"(max-width: 596px) 100vw, 596px\" \/><\/a><\/p>\n<p>where<strong> a<\/strong> is the<strong> real width<\/strong> of the reactor and <strong>b<\/strong> is the outer dimension of the <strong>reflector<\/strong> (<strong>b<sub>ex<\/sub><\/strong> is the outer dimension, including the<a title=\"Vacuum Boundary Condition \u2013 Extrapolated Length\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/neutron-diffusion-theory\/vacuum-boundary-condition-extrapolated-length\/\"> extrapolation distance<\/a>). With problems involving two different diffusion media, the following <a title=\"Boundary Conditions \u2013 Diffusion Equation\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/neutron-diffusion-theory\/boundary-conditions-diffusion-equation\/\">boundary conditions <\/a>must be satisfied:<\/p>\n<p><strong>1,2. Interface Conditions<\/strong><\/p>\n<p>At interfaces between <strong>two different diffusion media<\/strong> (such as between the reactor core and the neutron reflector), on physical grounds, the <strong>neutron flux<\/strong> and the normal component of the <strong>neutron current<\/strong> must be <strong>continuous<\/strong>. In other words, \u03c6 and J are not allowed to show a jump.<\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/08\/interface-condition-equations.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-15249\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/08\/interface-condition-equations.png\" alt=\"interface condition - equations\" width=\"268\" height=\"120\" \/><\/a><\/p>\n<p>It must be added, as J must be continuous, the flux gradient will show a jump if the <a title=\"Diffusion Coefficient\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/neutron-diffusion-theory\/diffusion-coefficient\/\">diffusion coefficients <\/a>in both media differ from each other. Since the solution of these two diffusion equations requires four boundary conditions, we have to use two boundary conditions more.<\/p>\n<p><strong>3. Finite Flux Condition<\/strong><\/p>\n<p>The solution must be finite in those regions where the equation is valid, except perhaps at artificial singular points of a source distribution. \u00a0This boundary condition can be written mathematically as:<\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/08\/finite-flux-condition-equation.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-15248\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/08\/finite-flux-condition-equation.png\" alt=\"finite flux condition - equation\" width=\"192\" height=\"47\" \/><\/a><\/p>\n<p><strong>4. Vacuum Boundary Condition<\/strong><\/p>\n<p>The vacuum boundary condition requires the <strong>relative neutron flux<\/strong> near the boundary to have a <strong>slope<\/strong> of <strong>-1\/d<\/strong>, i.e., the flux would extrapolate linearly to 0 at a distance d beyond the boundary (d is the extrapolated length). This <strong>zero flux boundary condition<\/strong> is more straightforward, and it can be written mathematically as:<\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/10\/reflected-reactor-boundary.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-15583\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/10\/reflected-reactor-boundary.png\" alt=\"reflected-reactor-boundary\" width=\"130\" height=\"75\" \/><\/a><\/p>\n<p>If<strong> d<\/strong> is not negligible, the physical dimensions of the reactor are increased by d, and this condition can be written as \u03a6(a\/2 + b<sub>ex<\/sub>) = \u00a00.<\/p>\n<p>The <strong>solution in the core<\/strong> satisfying these boundary conditions is:<\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/10\/reflected-reactor-solution.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-15584\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/10\/reflected-reactor-solution.png\" alt=\"reflected-reactor-solution\" width=\"211\" height=\"52\" \/><\/a><\/p>\n<p style=\"text-align: center;\">where<\/p>\n<p style=\"text-align: center;\"><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/10\/reflected-reactor-geometric-factor.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-15585\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/10\/reflected-reactor-geometric-factor.png\" alt=\"reflected-reactor-geometric-factor\" width=\"187\" height=\"76\" \/><\/a><\/p>\n<p>The <strong>solution in the reflector<\/strong> satisfying these boundary conditions is:<\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/10\/reflected-reactor-solution-reflector.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-15586\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/10\/reflected-reactor-solution-reflector.png\" alt=\"reflected-reactor-solution-reflector\" width=\"292\" height=\"201\" \/><\/a><\/p>\n<figure id=\"attachment_15587\" aria-describedby=\"caption-attachment-15587\" style=\"width: 550px\" class=\"wp-caption aligncenter\"><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/10\/reflected-reactor-one-group.png\"><img loading=\"lazy\" class=\"size-full wp-image-15587\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/10\/reflected-reactor-one-group.png\" alt=\"Neutron flux in a finite slab reactor with and without reflector.\" width=\"560\" height=\"323\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/10\/reflected-reactor-one-group.png 560w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/10\/reflected-reactor-one-group-300x173.png 300w\" sizes=\"(max-width: 560px) 100vw, 560px\" \/><\/a><figcaption id=\"caption-attachment-15587\" class=\"wp-caption-text\">Neutron flux in a finite slab reactor according to the one-group method (with and without reflector).<\/figcaption><\/figure>\n<h2>Flux in a Reflected Thermal Reactor &#8211; Two-group Method<\/h2>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/10\/thermal-and-fast-constants-moderators.png\"><img loading=\"lazy\" class=\" size-full wp-image-15588 alignright\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/10\/thermal-and-fast-constants-moderators.png\" alt=\"thermal-and-fast-constants-moderators\" width=\"403\" height=\"341\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/10\/thermal-and-fast-constants-moderators.png 403w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/10\/thermal-and-fast-constants-moderators-300x254.png 300w\" sizes=\"(max-width: 403px) 100vw, 403px\" \/><\/a>It was pointed out, the <strong>one-group method<\/strong> may provide reasonable results for the reactor, but this method does not accurately predict the flux. The energy of neutrons must be grouped into <strong>at least two groups<\/strong> to be<strong> more accurate<\/strong>. The two-group energy model leads to very interesting and important results that must be considered in the design of nuclear reactors.<\/p>\n<p>In this method, the entire range of neutron energies is divided into 2 intervals (<strong>fast<\/strong> and <strong>thermal groups<\/strong>). All neutrons within each interval are lumped into a group, and in this group, all parameters such as the <a title=\"Diffusion Coefficient\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/neutron-diffusion-theory\/diffusion-coefficient\/\"><strong>diffusion coefficients<\/strong><\/a> or <strong><a title=\"Neutron Cross-section\" href=\"http:\/\/sitepourvtc.com\/neutron-cross-section\/\">cross-sections<\/a> are averaged<\/strong>.<\/p>\n<p>To find the solution<strong> in a reactor core<\/strong> and <strong>a reflector<\/strong>, it is necessary to solve the following <strong>diffusion equations<\/strong> for the fast and thermal energy groups are:<\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/10\/reflected-reactor-two-group-method.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-15589\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/10\/reflected-reactor-two-group-method.png\" alt=\"reflected-reactor-two-group-method\" width=\"564\" height=\"670\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/10\/reflected-reactor-two-group-method.png 564w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/10\/reflected-reactor-two-group-method-253x300.png 253w\" sizes=\"(max-width: 564px) 100vw, 564px\" \/><\/a><\/p>\n<p>The solution of this system of homogeneous algebraic equations leads to a <strong>determinant of the coefficients<\/strong>. Such solution is shown in:<\/p>\n<p>Reference: Ragheb, M. TWO GROUP DIFFUSION THEORY FOR BARE AND REFLECTED REACTORS, University of Illinois, 2006.<\/p>\n<p>One of the striking results of such a solution is that the <strong>thermal flux<\/strong> reaches<strong> a local maximum<\/strong> near the core-reflector interface. This behavior cannot be derived using the one-group diffusion method because it is caused just by the thermalization of fast neutrons. The fast neutrons produced in the core can enter the reflector at high energy and are not absorbed as quickly in the reflector as neutrons thermalizing in the core because <a title=\"Neutron Absorption Cross-section\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-engineering-fundamentals\/neutron-nuclear-reactions\/neutron-absorption\/neutron-absorption-cross-section\/\">absorption cross-sections<\/a> in the <a title=\"Neutron Reflector\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-reactor\/neutron-reflector\/\">reflector<\/a> are much smaller than in the core (due to the absence of fuel). The thermal neutrons accumulate then near the core-reflector interface, resulting in the local maximum, usually known as the <strong>reflector peak<\/strong>. This also reduces the non-uniformity of the power distribution in the peripheral fuel assemblies and reduces <a title=\"Neutron Leakage\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/neutron-diffusion-theory\/neutron-leakage\/\">neutron leakage<\/a>, i.e., increases k<sub>eff<\/sub> of the system (or reduces the critical size of the reactor). This effect can be seen in the following figure.<\/p>\n<p>The <strong>reflector peak<\/strong> can be seen only in thermal flux within the reflector. It is found that the fast-flux does not show recovery peaks in the reflector but rather drops off sharply inside the reflector (due to thermalization and absorption).<\/p>\n<figure id=\"attachment_15562\" aria-describedby=\"caption-attachment-15562\" style=\"width: 564px\" class=\"wp-caption aligncenter\"><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/10\/Two-Group-Method-Reflected-Reactor.png\"><img loading=\"lazy\" class=\"size-full wp-image-15562\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/10\/Two-Group-Method-Reflected-Reactor.png\" alt=\"two-group-method-reflected-reactor\" width=\"574\" height=\"323\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/10\/Two-Group-Method-Reflected-Reactor.png 574w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/10\/Two-Group-Method-Reflected-Reactor-300x169.png 300w\" sizes=\"(max-width: 574px) 100vw, 574px\" \/><\/a><figcaption id=\"caption-attachment-15562\" class=\"wp-caption-text\">This figure shows the general effect of reflection in the thermal reactor system. Note that a reflector can raise the power density of the core-periphery and thus increase the core average power level without changing the peak power.<\/figcaption><\/figure>\n<h2>Reflector Savings<\/h2>\n<p>The <a title=\"Neutron Reflector\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-reactor\/neutron-reflector\/\"><strong>neutron reflector<\/strong><\/a> scatters back (or reflects) into the core many <a title=\"Neutron\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/atomic-nuclear-physics\/fundamental-particles\/neutron\/\">neutrons<\/a> that would otherwise escape. The neutrons reflected back into the core are available for a <a title=\"Nuclear Fission Chain Reaction\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-fission-chain-reaction\/\">chain reaction<\/a>. This means that the <strong>minimum critical size<\/strong> of the reactor is <strong>reduced<\/strong>. Alternatively, if the core size is maintained, the reflector makes additional reactivity available for higher fuel burnup. The<strong> decrease in the critical size<\/strong> of the core required is known as <strong>reflector savings<\/strong>. The <strong>concept of reflector savings<\/strong> is very important in many reactor calculations.<\/p>\n<p>It can be derived that there is a difference in the reflected and unreflected critical dimensions of a reactor. This difference is known as the <strong>reflector savings<\/strong>, it is denoted by \u03b4, and for infinite slab reactor, it is determined by:<\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/10\/reflector-savings-infinite.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-15590\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/10\/reflector-savings-infinite.png\" alt=\"reflector-savings-infinite\" width=\"487\" height=\"56\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/10\/reflector-savings-infinite.png 487w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/10\/reflector-savings-infinite-300x34.png 300w\" sizes=\"(max-width: 487px) 100vw, 487px\" \/><\/a><\/p>\n<p>according to this formula, the <strong>reflector savings<\/strong> as a function of the<strong> reflector thickness T<\/strong> can be calculated. As can be seen, reflector savings are a function of the thickness, and the reflector savings has a finite value for an infinitely thick reflector, where:<\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/10\/reflector-savings-finite.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-15591\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/10\/reflector-savings-finite.png\" alt=\"reflector-savings-finite\" width=\"421\" height=\"60\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/10\/reflector-savings-finite.png 421w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/10\/reflector-savings-finite-300x43.png 300w\" sizes=\"(max-width: 421px) 100vw, 421px\" \/><\/a><\/p>\n<p>This can be interpreted as follows: when the neutron reflector has a thickness of a few <a title=\"Diffusion Length\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/neutron-diffusion-theory\/diffusion-length\/\">diffusion lengths<\/a>, the probability that neutrons that have come into the outer shell of the neutron reflector are scattered back to the core is very small, so that an even thicker reflector hardly yields extra savings.<\/p>\n<p>These effects, however, become less significant as the size of the reactor, measured in <a title=\"Migration Length \u2013 Migration Area\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/neutron-diffusion-theory\/migration-length-migration-area\/\">migration lengths<\/a>, increases. The reflector savings amounts to a smaller fraction of the core dimension as its size becomes larger.<\/p>\n<p>Adding a reflector to a reactor allows either the volume of the reactor or the requirements on fuel to be reduced or some combination of the two. <strong>If the reflector savings is known<\/strong>, the calculation of the critical dimensions of a reflected reactor needs only the solution of the <strong>bare reactor<\/strong>, which is a <strong>simpler problem<\/strong>. For example, it is only necessary for the cylindrical reactor to determine the bare critical radius R<sub>0<\/sub> and the reflected radius is simply <strong>R = R<sub>0<\/sub> &#8211; \u03b4<\/strong>, where R<sub>0<\/sub> \u00a0is the critical diameter of a bare reactor.<\/p>\n<h2>Reflector Thickness<\/h2>\n<p>Logically, the <a title=\"Albedo Boundary Condition\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/neutron-diffusion-theory\/albedo-boundary-condition\/\"><strong>reflector coefficient (albedo)<\/strong><\/a> increases as the <strong>reflector thickness<\/strong> increases. But how thick should a reflector be? From an engineering point of view, reflectors are, of course, limited by certain reactor designs (e.g.,, by the width of the <a title=\"Reactor Pressure Vessel\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-reactor\/reactor-pressure-vessel\/\">reactor pressure vessel<\/a>). But, in general, very little is to be gained by increasing the thickness of the reflector <strong>beyond a value of 2L<\/strong> (2 x <a title=\"Diffusion Length\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/neutron-diffusion-theory\/diffusion-length\/\">diffusion length<\/a>).<\/p>\n<p>With<strong> H<sub>2<\/sub>0,<\/strong> a thickness of 2L is only about <strong>5 cm<\/strong>, whereas, for <strong>D<sub>2<\/sub>0,<\/strong> it is about <strong>300 cm<\/strong>. It would require a considerable amount of D<sub>2<\/sub>0 to extend the moderator by 300 cm since this additional D<sub>2<\/sub>0 is being placed on the outside of the core. From these values, it is obvious the <strong>neutron reflector plays a crucial role in heavy water or graphite reactors<\/strong>, in which the <a title=\"Neutron Leakage\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/neutron-diffusion-theory\/neutron-leakage\/\">neutron leakage <\/a>is higher than in <a title=\"LWR \u2013 Light Water Reactor\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/reactor-types\/lwr-light-water-reactor\/\">LWRs<\/a>.<\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/02\/Neutron-Moderators-Parameters.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-13684\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/02\/Neutron-Moderators-Parameters.png\" alt=\"Neutron Moderators - Parameters\" width=\"666\" height=\"510\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/02\/Neutron-Moderators-Parameters.png 666w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/02\/Neutron-Moderators-Parameters-300x230.png 300w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/02\/Neutron-Moderators-Parameters-180x138.png 180w\" sizes=\"(max-width: 666px) 100vw, 666px\" \/><\/a><\/p>\n<h2>Reflector Effects on Reactor Kinetics<\/h2>\n<p><strong>Reflector savings<\/strong> are not the only significant effect of the <strong>neutron reflector<\/strong> in reactor cores. The neutron reflector also influences the <strong><a title=\"Mean Generation Time with Delayed Neutrons\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/fission\/delayed-neutrons\/mean-generation-time-with-delayed-neutrons\/\">mean generation time<\/a><\/strong> and therefore influences the <strong>reactor kinetics<\/strong>.<\/p>\n<p>In the effect of a reflector on reactor kinetics, we are concerned with the <strong>time the neutrons spend in the reflector<\/strong> before returning to the core. In a thermal reactor, a reflector is generally chosen to help moderate the neutrons. Consequently, the neutrons that leak out of the core as thermal, epithermal, and fast neutrons are reflected back into the core as thermalized neutrons.<\/p>\n<p>Note that <strong>the <a title=\"Prompt Neutron Lifetime \u2013 PNL\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/fission\/prompt-neutrons\/prompt-neutron-lifetime-pnl\/\">prompt neutron lifetime<\/a>, l<\/strong>, is the <strong>average time from a prompt neutron emission<\/strong> to either <strong>its absorption<\/strong> (fission or radiative capture) or <strong>its escape<\/strong> from the system. In an infinite reactor (without escape), prompt neutron lifetime is the sum of <strong>the slowing downtime and the diffusion time<\/strong>.<\/p>\n<p><strong>l=t<\/strong><strong><sub>s<\/sub><\/strong><strong> + t<\/strong><strong><sub>d<\/sub><\/strong><\/p>\n<p>In an infinite thermal reactor <strong>t<\/strong><strong><sub>s<\/sub><\/strong><strong> &lt;&lt; t<\/strong><strong><sub>d<\/sub><\/strong> and therefore <strong>l \u2248 t<\/strong><strong><sub>d<\/sub><\/strong>. The typical prompt neutron lifetime <strong>in thermal reactors<\/strong> is on the order of<strong> 10<\/strong><strong><sup>\u22124<\/sup><\/strong><strong> seconds<\/strong>. <strong>The neutron lifetime with delayed neutrons<\/strong>, <strong>l<\/strong><strong><sub>d<\/sub><\/strong>, is the weighted average of the prompt generation times and a delayed neutron generation time. The delayed neutron generation time, <strong>\u03c4<\/strong>, is the weighted average of mean precursor lifetimes of the six groups (or more groups) of delayed neutron precursors.<\/p>\n<p>Because of the time delay in the process of diffusing in and out of the reflector, the kinetics effect of a reflector can be thought of as an <strong>effective increase in the neutron lifetime<\/strong> in the core under steady-state conditions or as an additionally delayed neutron precursor under transient operations.<\/p>\n<\/div>\n<div   id="8n9s8rpp6h"    class=\"su-divider su-divider-style-dotted\" style=\"margin:20px 0;border-width:2px;border-color:#999999\"><\/div>\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>Kenneth S. Krane. Introductory Nuclear Physics, 3rd Edition, Wiley, 1987,\u00a0ISBN:\u00a0978-0471805533<\/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>Nuclear Reactor<a href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-reactor\/\" 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>In previous chapters (nuclear chain reaction), it was derived that leakage of neutrons from the system significantly influences the criticality of a reactor. For thermal reactors, two variables are defined to describe the leakage process: fast non-leakage probability thermal non-leakage probability The fast non-leakage probability (Pf) and the thermal non-leakage probability (Pt) may be combined &#8230; <a title=\"Reflected Reactor\" class=\"read-more\" href=\"https:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/neutron-diffusion-theory\/reflected-reactor\/\" aria-label=\"More on Reflected Reactor\">Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":15150,"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\/15580"}],"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=15580"}],"version-history":[{"count":3,"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/pages\/15580\/revisions"}],"predecessor-version":[{"id":33776,"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/pages\/15580\/revisions\/33776"}],"up":[{"embeddable":true,"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/pages\/15150"}],"wp:attachment":[{"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/media?parent=15580"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}