{"id":4543,"date":"2026-08-19T15:34:37","date_gmt":"2026-08-19T07:34:37","guid":{"rendered":"https:\/\/www.ekaislot.com\/?p=4543"},"modified":"2026-08-19T15:46:53","modified_gmt":"2026-08-19T07:46:53","slug":"dynamic-stirred-tubular-reactor-principles-structure","status":"publish","type":"post","link":"https:\/\/www.ekaislot.com\/ru\/blog\/dynamic-stirred-tubular-reactor-principles-structure\/","title":{"rendered":"Dynamic Stirred Tubular Reactor (DTR)Principles &#038; Structure: An In-Depth Analysis"},"content":{"rendered":"<h2 class=\"wp-block-heading\">\ud83d\udd0d1. Which types of dynamic tubular reactors exist, and which is the focus?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">This article\u00a0<strong>centers on the <a href=\"https:\/\/www.ekaislot.com\/ru\/blog\/forced-continuous-tubular-reactor\/\">dynamic stirred tubular reactor (DTR)<\/a><\/strong>; the other two types will be covered separately.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><mark style=\"background-color:rgba(0, 0, 0, 0);color:#408d8e\" class=\"has-inline-color\">Three types of dynamic tubular reactors<\/mark><\/h3>\n\n\n\n<h4 class=\"wp-block-heading\">Dynamic Stirred Tubular Reactor (DTR)<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">Domestically known as the &#8220;dynamic tubular reactor,&#8221; suited to&nbsp;<strong>high-viscosity, solids-containing, coking-prone, long-residence-time<\/strong>&nbsp;processes (e.g., small-molecule solid\u2013liquid reactions, free-radical polymerization, polycondensation). Horizontal paddles \/ ribbons provide conveying and wall self-cleaning.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Taylor\u2013Couette Reactor<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">Suited to&nbsp;<strong>homogeneous \/ liquid\u2013liquid, low-to-medium viscosity, strongly exothermic<\/strong>&nbsp;systems with high shear-uniformity requirements (e.g., high-end polymerization, precision crystallization). Taylor vortices deliver uniform mixing and excellent heat transfer.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Oscillatory Baffled Reactor<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">Suited to processes&nbsp;<strong>sensitive to axial back-mixing, requiring precise residence-time-distribution control while suspending solids<\/strong>&nbsp;(e.g., continuous crystallization, enzyme catalysis, gas\u2013liquid reactions). Periodic oscillation and baffles achieve near-plug-flow with enhanced mass transfer.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Series arrangement:<\/strong>&nbsp;This series focuses on the dynamic stirred tubular reactor; the Taylor\u2013Couette reactor is treated in a standalone article; the oscillatory baffled reactor is introduced under the continuous-flow crystallization theme.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img alt=\"\" loading=\"lazy\" decoding=\"async\" width=\"800\" height=\"500\" src=\"https:\/\/www.ekaislot.com\/wp-content\/uploads\/1-48.jpg\" class=\"wp-image-4546\" srcset=\"https:\/\/www.ekaislot.com\/wp-content\/uploads\/1-48.jpg 800w, https:\/\/www.ekaislot.com\/wp-content\/uploads\/1-48-768x480.jpg 768w, https:\/\/www.ekaislot.com\/wp-content\/uploads\/1-48-18x12.jpg 18w\" sizes=\"auto, (max-width: 800px) 100vw, 800px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\">\ud83e\uddea 2. What is the theoretical basis of the DTR?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">The core is&nbsp;<strong>radial complete-mixing + axial plug flow<\/strong>, approaching ideal plug-flow behavior.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><mark style=\"background-color:rgba(0, 0, 0, 0);color:#408d8e\" class=\"has-inline-color\">Ideal Plug-Flow Reactor (PFR) model<\/mark><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">All fluid elements move at an identical velocity (no axial dispersion), with complete radial mixing; concentration and temperature vary only along the axis. The residence time equals the nominal residence time&nbsp;<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>\u03c4<\/mi><mo>=<\/mo><mi>V<\/mi><mrow data-mjx-texclass=\"ORD\"><mo>\/<\/mo><\/mrow><mi>Q<\/mi><\/math>&nbsp;(V = reactor volume, Q = volumetric flow rate).<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><mark style=\"background-color:rgba(0, 0, 0, 0);color:#408d8e\" class=\"has-inline-color\">Two deviations of real tubular reactors<\/mark><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Radial velocity gradient:<\/strong>\u00a0Under laminar flow this is a parabolic Poiseuille profile; velocity near the wall is far below that at the center \u2192 produces a residence-time distribution.<\/li>\n\n\n\n<li><strong>Axial back-mixing:<\/strong>\u00a0Molecular diffusion and turbulent mixing cause axial mixing of fluid elements at different reaction stages \u2192 blurs the concentration fronts.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Together these are called\u00a0<strong>axial dispersion<\/strong>, quantified by the\u00a0<strong>axial Peclet number (Peaxial)<\/strong>:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mi>P<\/mi><msub><mi>e<\/mi><mrow data-mjx-texclass=\"ORD\"><mi>a<\/mi><mi>x<\/mi><mi>i<\/mi><mi>a<\/mi><mi>l<\/mi><\/mrow><\/msub><mo>=<\/mo><mfrac><mrow><mi>u<\/mi><mi>L<\/mi><\/mrow><msub><mi>D<\/mi><mrow data-mjx-texclass=\"ORD\"><mi>a<\/mi><mi>x<\/mi><\/mrow><\/msub><\/mfrac><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">u = axial mean velocity, L = reactor length, D<sub>ax<\/sub>\u00a0= effective axial dispersion coefficient. Ideal plug flow: Pe \u2192 \u221e; continuous stirred-tank reactor (CSTR): Pe \u2192 0<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><mark style=\"background-color:rgba(0, 0, 0, 0);color:#408d8e\" class=\"has-inline-color\">DTR&#8217;s solution strategy<\/mark><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">A rotating agitator produces strong radial mixing \u2192 rapidly eliminating radial concentration and temperature gradients. When the rotational speed exceeds the critical speed, the radial mixing time is far smaller than the reaction time:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><msub><mi>\u03c4<\/mi><mrow data-mjx-texclass=\"ORD\"><mi>r<\/mi><mi>a<\/mi><mi>d<\/mi><mi>i<\/mi><mi>a<\/mi><mi>l<\/mi><\/mrow><\/msub><mo>=<\/mo><mfrac><msup><mi>R<\/mi><mn>2<\/mn><\/msup><msub><mi>D<\/mi><mrow data-mjx-texclass=\"ORD\"><mi>e<\/mi><mi>f<\/mi><mi>f<\/mi><mo>,<\/mo><mi>r<\/mi><mi>a<\/mi><mi>d<\/mi><mi>i<\/mi><mi>a<\/mi><mi>l<\/mi><\/mrow><\/msub><\/mfrac><mo>\u226a<\/mo><msub><mi>\u03c4<\/mi><mrow data-mjx-texclass=\"ORD\"><mi>r<\/mi><mi>e<\/mi><mi>a<\/mi><mi>c<\/mi><mi>t<\/mi><mi>i<\/mi><mi>o<\/mi><mi>n<\/mi><\/mrow><\/msub><mo>=<\/mo><mfrac><mn>1<\/mn><mi>k<\/mi><\/mfrac><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">R = tube radius, D<sub>eff,radial<\/sub>&nbsp;= mechanically enhanced effective radial dispersion coefficient.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u2192 Each cross-section can be treated as a well-mixed unit; only the axial direction retains a concentration gradient.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><mark style=\"background-color:rgba(0, 0, 0, 0);color:#408d8e\" class=\"has-inline-color\">Preservation of axial plug-flow behavior<\/mark><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Axial displacement of the fluid is set by the total feed flow rate. With a sound agitator design, the rotating turbulence intensifies radial mixing but&nbsp;<strong>does not significantly increase axial dispersion<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><mark style=\"background-color:rgba(0, 0, 0, 0);color:#408d8e\" class=\"has-inline-color\">Series-of-CSTRs model<\/mark><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">The DTR can be conceptualized as N well-mixed stages in series; the larger N is, the closer the behavior approaches ideal plug flow, with the relation:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mi>N<\/mi><mo>=<\/mo><mfrac><mrow><mi>P<\/mi><msub><mi>e<\/mi><mrow data-mjx-texclass=\"ORD\"><mi>a<\/mi><mi>x<\/mi><mi>i<\/mi><mi>a<\/mi><mi>l<\/mi><\/mrow><\/msub><\/mrow><mn>2<\/mn><\/mfrac><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">When&nbsp;<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>P<\/mi><msub><mi>e<\/mi><mrow data-mjx-texclass=\"ORD\"><mi>a<\/mi><mi>x<\/mi><mi>i<\/mi><mi>a<\/mi><mi>l<\/mi><\/mrow><\/msub><mo>=<\/mo><mn>100<\/mn><\/math>, this is equivalent to&nbsp;<strong>50 CSTRs in series<\/strong>, and near-ideal plug flow is achievable in practice.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">In plain terms, a DTR is like stringing dozens of small reactors into a single tube \u2014 each one thoroughly mixed, yet the material as a whole is pushed forward step by step.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\ud83d\udcd0 3. How does the Axial Dispersion Model (ADM) quantify the DTR?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">The ADM is the&nbsp;<strong>most commonly used quantitative framework<\/strong>&nbsp;for characterizing non-ideal flow in tubular reactors.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><mark style=\"background-color:rgba(0, 0, 0, 0);color:#408d8e\" class=\"has-inline-color\">Governing equation (species A)<\/mark><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mfrac><mrow><mi>\u2202<\/mi><msub><mi>C<\/mi><mi>A<\/mi><\/msub><\/mrow><mrow><mi>\u2202<\/mi><mi>t<\/mi><\/mrow><\/mfrac><mo>=<\/mo><msub><mi>D<\/mi><mrow data-mjx-texclass=\"ORD\"><mi>a<\/mi><mi>x<\/mi><\/mrow><\/msub><mfrac><mrow><msup><mi>\u2202<\/mi><mn>2<\/mn><\/msup><msub><mi>C<\/mi><mi>A<\/mi><\/msub><\/mrow><mrow><mi>\u2202<\/mi><msup><mi>z<\/mi><mn>2<\/mn><\/msup><\/mrow><\/mfrac><mo>\u2212<\/mo><mi>u<\/mi><mfrac><mrow><mi>\u2202<\/mi><msub><mi>C<\/mi><mi>A<\/mi><\/msub><\/mrow><mrow><mi>\u2202<\/mi><mi>z<\/mi><\/mrow><\/mfrac><mo>+<\/mo><msub><mi>r<\/mi><mi>A<\/mi><\/msub><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">C<sub>A<\/sub>&nbsp;= concentration of species A, z = axial coordinate, u = axial mean velocity, D<sub>ax<\/sub>&nbsp;= axial dispersion coefficient, r<sub>A<\/sub>&nbsp;= reaction rate.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><mark style=\"background-color:rgba(0, 0, 0, 0);color:#408d8e\" class=\"has-inline-color\">Steady-state simplification<\/mark><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">With the time derivative set to zero, the equation becomes a second-order ordinary differential equation:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><msub><mi>D<\/mi><mrow data-mjx-texclass=\"ORD\"><mi>a<\/mi><mi>x<\/mi><\/mrow><\/msub><mfrac><mrow><msup><mi>d<\/mi><mn>2<\/mn><\/msup><msub><mi>C<\/mi><mi>A<\/mi><\/msub><\/mrow><mrow><mi>d<\/mi><msup><mi>z<\/mi><mn>2<\/mn><\/msup><\/mrow><\/mfrac><mo>\u2212<\/mo><mi>u<\/mi><mfrac><mrow><mi>d<\/mi><msub><mi>C<\/mi><mi>A<\/mi><\/msub><\/mrow><mrow><mi>d<\/mi><mi>z<\/mi><\/mrow><\/mfrac><mo>+<\/mo><msub><mi>r<\/mi><mi>A<\/mi><\/msub><mo>=<\/mo><mn>0<\/mn><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><mark style=\"background-color:rgba(0, 0, 0, 0);color:#408d8e\" class=\"has-inline-color\">Boundary conditions<\/mark><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u0421\u0430\u0439\u0442&nbsp;<strong>Danckwerts boundary conditions<\/strong>&nbsp;describe the inlet and outlet diffusive fluxes:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Inlet (z = 0):\u00a0<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>u<\/mi><msub><mi>C<\/mi><mrow data-mjx-texclass=\"ORD\"><mi>A<\/mi><mn>0<\/mn><\/mrow><\/msub><mo>=<\/mo><mi>u<\/mi><msub><mi>C<\/mi><mi>A<\/mi><\/msub><msub><mrow data-mjx-texclass=\"ORD\"><mo stretchy=\"false\">|<\/mo><\/mrow><mrow data-mjx-texclass=\"ORD\"><mi>z<\/mi><mo>=<\/mo><msup><mn>0<\/mn><mo>+<\/mo><\/msup><\/mrow><\/msub><mo>\u2212<\/mo><msub><mi>D<\/mi><mrow data-mjx-texclass=\"ORD\"><mi>a<\/mi><mi>x<\/mi><\/mrow><\/msub><mfrac><mrow><mi>d<\/mi><msub><mi>C<\/mi><mi>A<\/mi><\/msub><\/mrow><mrow><mi>d<\/mi><mi>z<\/mi><\/mrow><\/mfrac><msub><mo stretchy=\"false\">|<\/mo><mrow data-mjx-texclass=\"ORD\"><mi>z<\/mi><mo>=<\/mo><msup><mn>0<\/mn><mo>+<\/mo><\/msup><\/mrow><\/msub><\/math><\/li>\n\n\n\n<li>Outlet (z = L):\u00a0<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mfrac><mrow><mi>d<\/mi><msub><mi>C<\/mi><mi>A<\/mi><\/msub><\/mrow><mrow><mi>d<\/mi><mi>z<\/mi><\/mrow><\/mfrac><msub><mrow data-mjx-texclass=\"ORD\"><mo stretchy=\"false\">|<\/mo><\/mrow><mrow data-mjx-texclass=\"ORD\"><mi>z<\/mi><mo>=<\/mo><mi>L<\/mi><\/mrow><\/msub><mo>=<\/mo><mn>0<\/mn><\/math><\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\"><mark style=\"background-color:rgba(0, 0, 0, 0);color:#408d8e\" class=\"has-inline-color\">First-order irreversible reaction \u2014 analytical solution (r<sub>A<\/sub>\u00a0= \u2212kC<sub>A<\/sub>)<\/mark><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mfrac><mrow><msub><mi>C<\/mi><mi>A<\/mi><\/msub><mo stretchy=\"false\">(<\/mo><mi>L<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><msub><mi>C<\/mi><mrow data-mjx-texclass=\"ORD\"><mi>A<\/mi><mn>0<\/mn><\/mrow><\/msub><\/mfrac><mo>=<\/mo><mfrac><mrow><mn>4<\/mn><mi>\u03b1<\/mi><mi>exp<\/mi><mo data-mjx-texclass=\"NONE\">\u2061<\/mo><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">(<\/mo><mfrac><mrow><mi>P<\/mi><mi>e<\/mi><\/mrow><mn>2<\/mn><\/mfrac><mo data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><\/mrow><mrow><mo stretchy=\"false\">(<\/mo><mn>1<\/mn><mo>+<\/mo><mi>\u03b1<\/mi><msup><mo stretchy=\"false\">)<\/mo><mn>2<\/mn><\/msup><mi>exp<\/mi><mo data-mjx-texclass=\"NONE\">\u2061<\/mo><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">(<\/mo><mfrac><mrow><mi>\u03b1<\/mi><mi>P<\/mi><mi>e<\/mi><\/mrow><mn>2<\/mn><\/mfrac><mo data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><mo>\u2212<\/mo><mo stretchy=\"false\">(<\/mo><mn>1<\/mn><mo>\u2212<\/mo><mi>\u03b1<\/mi><msup><mo stretchy=\"false\">)<\/mo><mn>2<\/mn><\/msup><mi>exp<\/mi><mo data-mjx-texclass=\"NONE\">\u2061<\/mo><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">(<\/mo><mfrac><mrow><mo>\u2212<\/mo><mi>\u03b1<\/mi><mi>P<\/mi><mi>e<\/mi><\/mrow><mn>2<\/mn><\/mfrac><mo data-mjx-texclass=\"CLOSE\">)<\/mo><\/mrow><\/mrow><\/mfrac><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">where&nbsp;<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>\u03b1<\/mi><mo>=<\/mo><msqrt><mn>1<\/mn><mo>+<\/mo><mfrac><mrow><mn>4<\/mn><mi>k<\/mi><mi>\u03c4<\/mi><\/mrow><mrow><mi>P<\/mi><mi>e<\/mi><\/mrow><\/mfrac><\/msqrt><\/math>, and Pe = uL\/D<sub>ax<\/sub>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Core conclusion:<\/strong>&nbsp;For a given Damk\u00f6hler number (Da = k\u03c4), a&nbsp;<strong>higher Peclet number (smaller axial dispersion) yields a higher conversion<\/strong>.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u2696\ufe0f 4. How do CSTR and PFR volume requirements compare?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">For the same feed and conversion, the&nbsp;<strong>PFR requires far less volume than the CSTR<\/strong>, though industrial design must weigh multiple factors.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><mark style=\"background-color:rgba(0, 0, 0, 0);color:#408d8e\" class=\"has-inline-color\">Design equations (isothermal, steady-state, ideal flow; rate decreases monotonically with conversion)<\/mark><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>CSTR:\u00a0<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>V<\/mi><mrow data-mjx-texclass=\"ORD\"><mi>C<\/mi><mi>S<\/mi><mi>T<\/mi><mi>R<\/mi><\/mrow><\/msub><mo>=<\/mo><mfrac><mrow><msub><mi>F<\/mi><mrow data-mjx-texclass=\"ORD\"><mi>A<\/mi><mn>0<\/mn><\/mrow><\/msub><mi>X<\/mi><\/mrow><mrow><mo>\u2212<\/mo><msub><mi>r<\/mi><mrow data-mjx-texclass=\"ORD\"><mi>A<\/mi><mo>,<\/mo><mi>e<\/mi><mi>x<\/mi><mi>i<\/mi><mi>t<\/mi><\/mrow><\/msub><\/mrow><\/mfrac><\/math><\/li>\n\n\n\n<li>PFR:\u00a0<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>V<\/mi><mrow data-mjx-texclass=\"ORD\"><mi>P<\/mi><mi>F<\/mi><mi>R<\/mi><\/mrow><\/msub><mo>=<\/mo><msub><mi>F<\/mi><mrow data-mjx-texclass=\"ORD\"><mi>A<\/mi><mn>0<\/mn><\/mrow><\/msub><msubsup><mo data-mjx-texclass=\"OP\">\u222b<\/mo><mn>0<\/mn><mi>X<\/mi><\/msubsup><mfrac><mrow><mi>d<\/mi><mi>X<\/mi><\/mrow><mrow><mo>\u2212<\/mo><msub><mi>r<\/mi><mi>A<\/mi><\/msub><\/mrow><\/mfrac><\/math><\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\"><mark style=\"background-color:rgba(0, 0, 0, 0);color:#408d8e\" class=\"has-inline-color\">Reason for the volume difference<\/mark><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">The PFR maintains high upstream reaction rates throughout its length; the CSTR operates its entire volume at the lowest (exit) rate \u2192&nbsp;<strong>V<sub>CSTR<\/sub>&nbsp;&gt; V<sub>PFR<\/sub><\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><mark style=\"background-color:rgba(0, 0, 0, 0);color:#408d8e\" class=\"has-inline-color\">First-order irreversible reaction \u2014 quantitative comparison (constant density, \u2212r<sub>A<\/sub>\u00a0= kC<sub>A<\/sub>\u00a0= kC<sub>A0<\/sub>(1\u2212X))<\/mark><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mfrac><msub><mi>V<\/mi><mrow data-mjx-texclass=\"ORD\"><mi>C<\/mi><mi>S<\/mi><mi>T<\/mi><mi>R<\/mi><\/mrow><\/msub><msub><mi>V<\/mi><mrow data-mjx-texclass=\"ORD\"><mi>P<\/mi><mi>F<\/mi><mi>R<\/mi><\/mrow><\/msub><\/mfrac><mo>=<\/mo><mfrac><mrow><mi>X<\/mi><mrow data-mjx-texclass=\"ORD\"><mo>\/<\/mo><\/mrow><mo stretchy=\"false\">(<\/mo><mn>1<\/mn><mo>\u2212<\/mo><mi>X<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><mrow><mo>\u2212<\/mo><mi>ln<\/mi><mo data-mjx-texclass=\"NONE\">\u2061<\/mo><mo stretchy=\"false\">(<\/mo><mn>1<\/mn><mo>\u2212<\/mo><mi>X<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><\/mfrac><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">At conversion X = 0.9,&nbsp;<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mfrac><msub><mi>V<\/mi><mrow data-mjx-texclass=\"ORD\"><mi>C<\/mi><mi>S<\/mi><mi>T<\/mi><mi>R<\/mi><\/mrow><\/msub><msub><mi>V<\/mi><mrow data-mjx-texclass=\"ORD\"><mi>P<\/mi><mi>F<\/mi><mi>R<\/mi><\/mrow><\/msub><\/mfrac><mo>\u2248<\/mo><mn>3.91<\/mn><\/math>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u2192 At high conversion the CSTR volume demand is about&nbsp;<strong>4\u00d7<\/strong>&nbsp;that of the PFR.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Industrial-design supplement:<\/strong>\u00a0In practice one must also weigh\u00a0<strong>heat transfer, safety, <a href=\"https:\/\/www.ekaislot.com\/ru\/reactor-internal\/\">pressure drop<\/a>, back-mixing, mass-transfer limitations, and operational stability<\/strong>.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\ud83c\udfd7\ufe0f 5. What are the five core subsystems of the DTR?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">There are&nbsp;<strong>five core subsystems<\/strong>&nbsp;that must work in concert to deliver performance.<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th class=\"has-text-align-left\" data-align=\"left\">Subsystem<\/th><th class=\"has-text-align-left\" data-align=\"left\">Core function<\/th><th class=\"has-text-align-left\" data-align=\"left\">Key points<\/th><\/tr><\/thead><tbody><tr><td><strong><a href=\"https:\/\/www.ekaislot.com\/ru\/process-equipment\/\">External pressure vessel<\/a><\/strong><\/td><td>Primary pressure boundary + heat-transfer surface<\/td><td>Materials: 316L \/ 904L stainless steel, Hastelloy C-276, tantalum; inner diameter set by throughput + agitator design<\/td><\/tr><tr><td><strong>Rotating agitation assembly<\/strong><\/td><td>Core component enabling radial mixing<\/td><td>Mixing elements: paddle (low visc.), twisted ribbon (medium visc.), anchor (high visc.), specialty structures (dead-zone elimination);&nbsp;<strong>tip clearance is the key design parameter<\/strong><\/td><\/tr><tr><td><strong>Heat-transfer system<\/strong><\/td><td>Precise temperature control<\/td><td>Methods: jacket, hollow agitator shaft with circulating medium, internal coils\/tubes; independently zoned control<\/td><\/tr><tr><td><strong>Dynamic seal system<\/strong><\/td><td>Maintain pressure integrity<\/td><td>Types: mechanical face seal (single\/double cartridge), magnetic drive, packing seal;&nbsp;<strong>highest maintenance frequency<\/strong><\/td><\/tr><tr><td><strong>Drive &amp; control system<\/strong><\/td><td>Provide controllable speed<\/td><td>Speed range&nbsp;<strong>10\u2013500 RPM<\/strong>; VFD continuous adjustment; integrated speed, torque, and vibration monitoring<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\">\ud83d\udcdd 6. Supplementary details &amp; engineering trade-offs<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Naming clarification:<\/strong>\u00a0The domestically common term &#8220;dynamic tubular reactor&#8221; refers narrowly to the\u00a0<strong>dynamic stirred tubular reactor (DTR)<\/strong>, and broadly also includes the Taylor\u2013Couette and oscillatory baffled types.<\/li>\n\n\n\n<li><strong>Physical meaning of the Peclet number:<\/strong>\u00a0It is the ratio of convective to diffusive rate. The larger its value, the more the axial dispersion becomes negligible relative to the bulk flow, and the closer the reactor approaches plug flow.<\/li>\n\n\n\n<li><strong>Dual effect of tip clearance:<\/strong>\u00a0Too small a clearance risks wall scoring and poor mechanical stability; too large reduces mixing efficiency and promotes wall coking \u2014 a core design trade-off.<\/li>\n<\/ul>","protected":false},"excerpt":{"rendered":"<p>\ud83d\udd0d1. Which types of dynamic tubular reactors exist, and which is the focus? This article\u00a0centers on the dynamic stirred tubular reactor (DTR); the other two types will be covered separately. Three types of dynamic tubular reactors Dynamic Stirred Tubular Reactor (DTR) Domestically known as the &#8220;dynamic tubular reactor,&#8221; suited to&nbsp;high-viscosity, solids-containing, coking-prone, long-residence-time&nbsp;processes (e.g., small-molecule [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":4545,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"_seopress_titles_title":"","_seopress_titles_desc":"","_seopress_robots_index":"","_seopress_robots_follow":"","_seopress_robots_imageindex":"","_seopress_robots_snippet":"","_seopress_robots_primary_cat":"","_seopress_robots_breadcrumbs":"","_seopress_robots_freeze_modified_date":"","_seopress_robots_custom_modified_date":"","_seopress_robots_canonical":"","_seopress_social_fb_title":"","_seopress_social_fb_desc":"","_seopress_social_fb_img":"","_seopress_social_fb_img_attachment_id":0,"_seopress_social_fb_img_width":0,"_seopress_social_fb_img_height":0,"_seopress_social_twitter_title":"","_seopress_social_twitter_desc":"","_seopress_social_twitter_img":"","_seopress_social_twitter_img_attachment_id":0,"_seopress_social_twitter_img_width":0,"_seopress_social_twitter_img_height":0,"_seopress_redirections_value":"","_seopress_redirections_enabled":"","_seopress_redirections_enabled_regex":"","_seopress_redirections_logged_status":"","_seopress_redirections_param":"","_seopress_redirections_type":0,"_seopress_analysis_target_kw":"","_seopress_news_disabled":"","_seopress_video_disabled":"","_seopress_video":[],"_seopress_pro_schemas_manual":[],"_seopress_pro_rich_snippets_disable_all":"","_seopress_pro_rich_snippets_disable":[],"_seopress_pro_schemas":[],"footnotes":""},"categories":[1],"tags":[],"class_list":["post-4543","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-blog"],"acf":[],"_links":{"self":[{"href":"https:\/\/www.ekaislot.com\/ru\/wp-json\/wp\/v2\/posts\/4543","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.ekaislot.com\/ru\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.ekaislot.com\/ru\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.ekaislot.com\/ru\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.ekaislot.com\/ru\/wp-json\/wp\/v2\/comments?post=4543"}],"version-history":[{"count":3,"href":"https:\/\/www.ekaislot.com\/ru\/wp-json\/wp\/v2\/posts\/4543\/revisions"}],"predecessor-version":[{"id":4550,"href":"https:\/\/www.ekaislot.com\/ru\/wp-json\/wp\/v2\/posts\/4543\/revisions\/4550"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.ekaislot.com\/ru\/wp-json\/wp\/v2\/media\/4545"}],"wp:attachment":[{"href":"https:\/\/www.ekaislot.com\/ru\/wp-json\/wp\/v2\/media?parent=4543"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.ekaislot.com\/ru\/wp-json\/wp\/v2\/categories?post=4543"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.ekaislot.com\/ru\/wp-json\/wp\/v2\/tags?post=4543"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}