<?xml version="1.0" encoding="ISO-8859-1"?><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<front>
<journal-meta>
<journal-id>0122-5383</journal-id>
<journal-title><![CDATA[CT&F - Ciencia, Tecnología y Futuro]]></journal-title>
<abbrev-journal-title><![CDATA[C.T.F Cienc. Tecnol. Futuro]]></abbrev-journal-title>
<issn>0122-5383</issn>
<publisher>
<publisher-name><![CDATA[Instituto Colombiano del Petróleo (ICP) - ECOPETROL S.A.]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S0122-53832016000200057</article-id>
<article-id pub-id-type="doi">10.29047/01225383.03</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[RIGOROUS ANALYTICAL SOLUTION OF THE BASIC CONCENTRATION MODEL FOR AN INJECTED FLUID IN A PIPE]]></article-title>
<article-title xml:lang="es"><![CDATA[Solución analítica rigurosa del modelo básico de concentración para un fluido inyectado en un tubo]]></article-title>
<article-title xml:lang="pt"><![CDATA[Solução analítica rigorosa do modelo básico de concentração para um fluído injetado em um tubo]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Suárez]]></surname>
<given-names><![CDATA[Edgardo-Jonathan]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
<xref ref-type="aff" rid="Aaf"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Rodríguez]]></surname>
<given-names><![CDATA[Alejandro]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Chávez]]></surname>
<given-names><![CDATA[Ángel-Enrique]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Izquierdo]]></surname>
<given-names><![CDATA[Elena]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Palacio]]></surname>
<given-names><![CDATA[Arturo]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad Nacional Autónoma de México  ]]></institution>
<addr-line><![CDATA[ D.F]]></addr-line>
<country>Mexico</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,Universidad Autónoma de Tamaulipas  ]]></institution>
<addr-line><![CDATA[Tampico ]]></addr-line>
<country>Mexico</country>
</aff>
<aff id="Af3">
<institution><![CDATA[,Universidad Nacional Autónoma de México Facultad de Química Departamento de Ingeniería Química]]></institution>
<addr-line><![CDATA[ D.F]]></addr-line>
<country>Mexico</country>
</aff>
<aff id="Af4">
<institution><![CDATA[,Universidad de la Habana Facultad de Química Departamento de Química-Física]]></institution>
<addr-line><![CDATA[La Habana ]]></addr-line>
<country>Cuba</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>12</month>
<year>2016</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>12</month>
<year>2016</year>
</pub-date>
<volume>6</volume>
<numero>4</numero>
<fpage>57</fpage>
<lpage>66</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_arttext&amp;pid=S0122-53832016000200057&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_abstract&amp;pid=S0122-53832016000200057&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_pdf&amp;pid=S0122-53832016000200057&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract In the oil industry chemical products are often injected during fluid transport either to modify the rheological characteristics, i.e. viscosity, or to stabilize crude oil composition by inhibition of phase separation. The effects are generally related to the dosed product concentration so it is important to study the transient variation in the amount of fluid incorporated to a stream mainly for cases where there is no mechanical pre-mixing of phases when the main flow is in the laminar regime. This paper presents a theoretical model based on the conservation equations of mass and momentum that prescribes the temporal evolution of the spatial concentration profiles under different conditions. An analytical solution to the model is proposed that shows how the behavior is dependent on the injection method. The theoretical results can be considered as a basis to predict how the injection method affects these profiles.]]></p></abstract>
<abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen En la industria petrolera suelen inyectarse productos químicos durante el transporte de fluidos ya sea para modificar sus características reológicas, como la viscosidad, o para estabilizar su composición inhibiendo la separación de fases. Los efectos generalmente dependen de la concentración en la que se encuentre dosificado el producto, por lo que es relevante el estudio de la variación de la cantidad del fluido incorporado en el tiempo para los casos en los que no existe un mezclado mecánico de las fases y existe un régimen laminar. En este trabajo se desarrolló un modelo teórico basado en las ecuaciones de conservación de cantidad de movimiento y masa, que definen la evolución temporal de los perfiles espaciales de concentración bajo dos condiciones distintas. Se propone una solución analítica al modelo, y a partir del análisis se encuentra que el comportamiento del flujo es dependiente del tipo de inyección que se realice. Los resultados teóricos pueden ser tomados como base para predecir cómo el método de inyección afecta a estos perfiles.]]></p></abstract>
<abstract abstract-type="short" xml:lang="pt"><p><![CDATA[Resumo Na indústria petroleira a injeção de produtos químicos durante o transporte de fluidos é comumente utiliza seja para alterar suas características reológicas, como a viscosidade, ou para estabilizar sua composição inibindo a separação de fases. Os efeitos geralmente dependem da concentração de dosagem do produto. Por tanto, é relevante estudar a variação da quantidade do fluído incorporado no tempo para os casos onde não existe uma mistura mecânica das fases com presença de um regime laminar. Neste trabalho desenvolvemos um modelo teórico com base nas equações de conservação de quantidade de movimento e massa, que definem a evolução provisória dos perfis espaciais de concentração sob condições diferentes. Propõe-se uma solução analítica ao modelo e com base nessa análise, o comportamento do fluxo foi encontrado como sendo dependente do tipo de injeção a ser realizada. Os resultados teóricos podem ser tomados como base para predizer como o método de injeção afeta estes perfis.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[Concentration profile]]></kwd>
<kwd lng="en"><![CDATA[Homogeneous blend mix]]></kwd>
<kwd lng="en"><![CDATA[dimensionless model]]></kwd>
<kwd lng="es"><![CDATA[Perfil de concentración]]></kwd>
<kwd lng="es"><![CDATA[Mezcla homogénea]]></kwd>
<kwd lng="pt"><![CDATA[Perfil de concentração]]></kwd>
<kwd lng="pt"><![CDATA[Mistura homogénea]]></kwd>
</kwd-group>
</article-meta>
</front><back>
<ref-list>
<ref id="B1">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Abdulbari]]></surname>
<given-names><![CDATA[H. A]]></given-names>
</name>
<name>
<surname><![CDATA[Shabirin]]></surname>
<given-names><![CDATA[A]]></given-names>
</name>
<name>
<surname><![CDATA[Abdurrahman]]></surname>
<given-names><![CDATA[H. N]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Bio-polymers for improving liquid flow in pipelines-a review and future work opportunities]]></article-title>
<source><![CDATA[J. Ind. Engineer. Chem]]></source>
<year>2014</year>
<volume>20</volume>
<numero>4</numero>
<issue>4</issue>
<page-range>1157-70</page-range></nlm-citation>
</ref>
<ref id="B2">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Adams]]></surname>
<given-names><![CDATA[J.J]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Asphaltene adsorption, a literature review]]></article-title>
<source><![CDATA[Energ. Fuel]]></source>
<year>2014</year>
<volume>28</volume>
<numero>5</numero>
<issue>5</issue>
<page-range>2831-56</page-range></nlm-citation>
</ref>
<ref id="B3">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Barailler]]></surname>
<given-names><![CDATA[F.]]></given-names>
</name>
<name>
<surname><![CDATA[Heniche]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Tanguy]]></surname>
<given-names><![CDATA[P. A]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[CFD analysis of a rotor-stator mixer with viscous fluids]]></article-title>
<source><![CDATA[Chemical engineering science]]></source>
<year>2006</year>
<volume>61</volume>
<numero>9</numero>
<issue>9</issue>
<page-range>2888-94</page-range></nlm-citation>
</ref>
<ref id="B4">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Bird]]></surname>
<given-names><![CDATA[R. B.]]></given-names>
</name>
<name>
<surname><![CDATA[Stewart]]></surname>
<given-names><![CDATA[W. E.]]></given-names>
</name>
<name>
<surname><![CDATA[Lightfoot]]></surname>
<given-names><![CDATA[E. N]]></given-names>
</name>
</person-group>
<source><![CDATA[Transport Phenomena]]></source>
<year>2002</year>
<edition>2 Ed</edition>
<publisher-loc><![CDATA[New York ]]></publisher-loc>
<publisher-name><![CDATA[Jonh Wiley &amp; Son]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B5">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Centeno]]></surname>
<given-names><![CDATA[G.]]></given-names>
</name>
<name>
<surname><![CDATA[Sánchez-Reyna]]></surname>
<given-names><![CDATA[G.]]></given-names>
</name>
<name>
<surname><![CDATA[Ancheyta]]></surname>
<given-names><![CDATA[J]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Calculating the viscosity of crude oil blends by binary interaction parameters using literature data]]></article-title>
<source><![CDATA[Petrol. Science Technol]]></source>
<year>2015</year>
<volume>33</volume>
<numero>8</numero>
<issue>8</issue>
<page-range>893-900</page-range></nlm-citation>
</ref>
<ref id="B6">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Chae]]></surname>
<given-names><![CDATA[M. S.]]></given-names>
</name>
<name>
<surname><![CDATA[Chung]]></surname>
<given-names><![CDATA[B. J]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Laminar mixed-convection experiments in horizontal pipes and derivation of a semi-empirical buoyancy coefficient]]></article-title>
<source><![CDATA[Int. J. Therm. Sci]]></source>
<year>2014</year>
<volume>84</volume>
<page-range>335-46</page-range></nlm-citation>
</ref>
<ref id="B7">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Chandra]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
<name>
<surname><![CDATA[Chhabra]]></surname>
<given-names><![CDATA[R. P]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Laminar free convection from a horizontal semi-circular cylinder to power-law fluids]]></article-title>
<source><![CDATA[Int. J. Heat Mass Transfer]]></source>
<year>2012</year>
<volume>55</volume>
<numero>11</numero>
<issue>11</issue>
<page-range>2934-44</page-range></nlm-citation>
</ref>
<ref id="B8">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Daskopoulos]]></surname>
<given-names><![CDATA[P.]]></given-names>
</name>
<name>
<surname><![CDATA[Lenhoff]]></surname>
<given-names><![CDATA[A. M]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Dispersion coefficient for laminar flow in curved tubes]]></article-title>
<source><![CDATA[AIChE J]]></source>
<year>1988</year>
<volume>34</volume>
<numero>12</numero>
<issue>12</issue>
<page-range>2052-8</page-range></nlm-citation>
</ref>
<ref id="B9">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Gabrienko]]></surname>
<given-names><![CDATA[A. A.]]></given-names>
</name>
<name>
<surname><![CDATA[Subramani]]></surname>
<given-names><![CDATA[V.]]></given-names>
</name>
<name>
<surname><![CDATA[Martyanov]]></surname>
<given-names><![CDATA[O. N.]]></given-names>
</name>
<name>
<surname><![CDATA[Kazarian]]></surname>
<given-names><![CDATA[S. G]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Correlation between asphaltene stability in n-Heptane and crude oil composition revealed with In Situ chemical imaging]]></article-title>
<source><![CDATA[Adsorpt. Sci. Technol]]></source>
<year>2014</year>
<volume>32</volume>
<numero>4</numero>
<issue>4</issue>
<page-range>243-56</page-range></nlm-citation>
</ref>
<ref id="B10">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Hosseini-Dastgerdi]]></surname>
<given-names><![CDATA[Z.]]></given-names>
</name>
<name>
<surname><![CDATA[Tabatabaei-Nejad]]></surname>
<given-names><![CDATA[S. A. R.]]></given-names>
</name>
<name>
<surname><![CDATA[Sahraei]]></surname>
<given-names><![CDATA[E.]]></given-names>
</name>
<name>
<surname><![CDATA[Nowroozi]]></surname>
<given-names><![CDATA[H]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Morphology and size distribution characterization of precipitated asphaltene from live oil during pressure depletion]]></article-title>
<source><![CDATA[Journal of Dispersion Science and Technology]]></source>
<year>2015</year>
<volume>36</volume>
<numero>3</numero>
<issue>3</issue>
<page-range>363-8</page-range></nlm-citation>
</ref>
<ref id="B11">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Martínez-Palou]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
<name>
<surname><![CDATA[Mosqueira]]></surname>
<given-names><![CDATA[M. DL.]]></given-names>
</name>
<name>
<surname><![CDATA[Zapata-Rendón]]></surname>
<given-names><![CDATA[B.M.]]></given-names>
</name>
<name>
<surname><![CDATA[Mar-Juárez]]></surname>
<given-names><![CDATA[E.]]></given-names>
</name>
<name>
<surname><![CDATA[Bernal-Huicochea]]></surname>
<given-names><![CDATA[C.]]></given-names>
</name>
<name>
<surname><![CDATA[Clavel-López]]></surname>
<given-names><![CDATA[J. D. C.]]></given-names>
</name>
<name>
<surname><![CDATA[Aburto]]></surname>
<given-names><![CDATA[J]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Transportation of heavy and extra-heavy crude oil by pipeline: a review]]></article-title>
<source><![CDATA[J. Petrol. Sci. Engine]]></source>
<year>2011</year>
<volume>75</volume>
<numero>3</numero>
<issue>3</issue>
<page-range>274-82</page-range></nlm-citation>
</ref>
<ref id="B12">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Trivedi]]></surname>
<given-names><![CDATA[R. N.]]></given-names>
</name>
<name>
<surname><![CDATA[Vasudeva]]></surname>
<given-names><![CDATA[K]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Axial dispersion in laminar flow in helical coils]]></article-title>
<source><![CDATA[Chem. Engine. Sci]]></source>
<year>1975</year>
<volume>30</volume>
<numero>3</numero>
<issue>3</issue>
<page-range>317-25</page-range></nlm-citation>
</ref>
<ref id="B13">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Zendehboudi]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
<name>
<surname><![CDATA[Shafiei]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
<name>
<surname><![CDATA[Bahadori]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
<name>
<surname><![CDATA[James]]></surname>
<given-names><![CDATA[L. A.]]></given-names>
</name>
<name>
<surname><![CDATA[Elkamel]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
<name>
<surname><![CDATA[Lohi]]></surname>
<given-names><![CDATA[A]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Asphaltene precipitation and deposition in oil reservoirs-technical aspects, experimental and hybrid neural network predictive tools]]></article-title>
<source><![CDATA[Chem. Engine. Res. Design]]></source>
<year>2014</year>
<volume>92</volume>
<numero>5</numero>
<issue>5</issue>
<page-range>857-75</page-range></nlm-citation>
</ref>
<ref id="B14">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Xue-Yi]]></surname>
<given-names><![CDATA[Y.]]></given-names>
</name>
<name>
<surname><![CDATA[Zhang]]></surname>
<given-names><![CDATA[L. D.]]></given-names>
</name>
<name>
<surname><![CDATA[Zheng]]></surname>
<given-names><![CDATA[J. R]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[A double film model and its application to the stability of liquid-liquid stratified flow]]></article-title>
<source><![CDATA[Phys. Scripta]]></source>
<year>2014</year>
<volume>89</volume>
<numero>6</numero>
<issue>6</issue>
<page-range>65-101</page-range></nlm-citation>
</ref>
<ref id="B15">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Zhang]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[Xu]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
<name>
<surname><![CDATA[Li]]></surname>
<given-names><![CDATA[W]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[High shear mixers: a review of typical applications and studies on power draw, flow pattern, energy dissipation and transfer properties]]></article-title>
<source><![CDATA[Chem. Engine. Processing Process Intensify]]></source>
<year>2012</year>
<volume>57</volume>
<page-range>25-41</page-range></nlm-citation>
</ref>
</ref-list>
</back>
</article>
