Laminar akışlı adyabatik boru reaktörünün teorik incelenmesi

Abstract

ÖZET LAMİNAR AKIŞLI ADYABATİK BORU REAKTÖRÜNÜN TEORİK İNCELENMESİ Bu çalışmada laminar akışlı adyabatik boru reaktöründe etilenin hidrojenlenmesi modeli esas alınmıştır. Laminar akış esası altında akışı, enerjiyi ve difuzyonu tanımla yan ve ekzakt çözümü belirleyen matematiksel eşitlikler türetilmiştir. Bu eşitliklerde aktivasyon enerjisi yer almaktadır. Şimdiye kadarki uy gulamalarda büyüklüklerin tayini konusunda izoterm koşulu seçilmektedir. Böyle bir seçimle matematiksel tanımda beliren aktivasyon enerjisi elimine edilmiş olmaktadır. Bu yolla yapılan ölçmeler izoterm reaktörü belirleyen basit matematiksel ifadelerle değerlendirilmektedir. İzoterm koşulunu sağlayabilmek için çalışmalarda, reaktan konsantrasyonu çok küçük alınmakta, ölçme hataları neticeyi önemli ölçüde etkilemektedir. Bu nedenle literatürde reaksiyon kinetiği konusunda çelişkili neticelere rastlanmaktadır. Sunulan çalışmada reaksiyonu belirleyen Damköhler sayısı (Dag) yerine, aktivasyon enerjisini elimine eden bir ortalama Damköhler sayısı (Da) tanımı yapılarak izotermal olmayan şartlarda, büyük reaktan konsantrasyonu değerleri için adyabatik reaktör matematiksel olarak tanımlanmıştır. Böylece adyabatik boru reaktöründe etilen hidrojenlen mesi model reaksiyonu için ekzakt ve belirlenen bu yeni yöntemle yaklaşık olarak hesaplanmış} elde edilen sonuçların tam bir uyum içinde olduğu görülmüştür. Takdim edilen matematiksel tanımda sadece ortalama Damköhler sayısı (Da) parametre olarak belirdiğinden herhangi bir ekzoterm gaz reaksiyonu için çeşitli Da değerlerinde denklem takımı çözülerek dönüşüm diyagramları hazırlanır. Hazırlanan bu diyagramlar yardımıyla dönüşüm ölçme değerlerine ait da. değerleri belirlenir ve buradan da reaksiyon hız sabiti değerleri hesaplanır. İlgili sıcaklık T = 0.5 (T0+Tad ) şeklinde tanımlandığından, en küçük kareler yöntemiyle aktivasyon enerjisi ve frekans faktörü sağlıklı olarak belirlenebilir. Bu çalışmada ayrıca, propilen ve bütilen hidrojenlenmesi reaksiyonları için önerilen yaklaşık çözüm yöntemiyle hesaplanan dönüşüm diyagramları da verilmiştir. X

SUMMARY A THEORETICAL INVESTIGATION OF THE LAMINAR FLOW ADIABATIC TUBULAR REACTOR The pure and Tenewable energy source's need to be stored be cause of their comparatively low and variable potential. Storage of energy presents a very difficult problem. From this point of view, the use of hydrogen energy seems to have the least number of problems. Hydrogen is pure and nonpoisonous, however due to its high diffusive nature, it is extremely diffucult to store this element. There fore instead of storing pure hydrogen, it is recommended to store this substance by hydrogenating the unsaturated hydrocarbons. It is also possible to increase the heat capacity in this manner. The firs problem encountered in the process of investigating the balance between the energy and mass in the hydrogenation reac tor, is to determine the chemical reaction associated with hydrogena tion in the hydrogenation reactor. This Study aims to develope the background that shall be useful in future experimental studies to determine the activation energy and the frequency factor in a correct manner. Hydrogenous catalytic gas reactions occur on solid surfaces known as catalysts. Reaction occurs in two distinct stages. In the first stage, reactants in gaseous form diffuse into the hard surface of the catalyst and is adsorbed by the active spots. The reaction now ter minates and the products of the reaction become conspicuous. Shortly after, the products are desorbed, leave the hard surface and are con verted into the gaseous form. In technical practice, in order to do the analysis and calcula tions relating to the chemical conversion in a reactor, it is essential to know the values known as the activation energy and the frequency factor. According to the equation of Arrhenius, the ratio and the cons tant of reaction can be determined: k = Ar.i -EA/RT XIwhere E. is the activation energy A, is the frequency factor The reaction-kinetic value is determined in adiabatic tubulars containing noncatalytic material under various conditions of chemical conversion. These measured values are shown in proper mathematical terms suitable for the conditions under which the measurements were performed. The mathematical model of a tubular reactor is generally made by using the equations of conservation of momentum, mass and heat. In steady tubular reactors, variation of mole quantity (concent ration) and temperature cause changes in axial velocity together with the appearance of radial convection currents. Consequently, in order to calculate radial and axial velocities in laminar flow, reactors, use of Navier-Stokes equations are made. Due to the decrease of the mole quantity, the expansion term is neglected. In addition to this, the simplified process of Pramidtl is applied and equality of pressure in radial direction is assumed. To calculate the radial velocity the equation of continuity is used. In forming the equations for the transfer of mass, mass trans fer in three directions was taken into consideration. Axial and ther- modiffusion were neglected and the ternery diffusion coefficients, DAC ant^ ^CA were ta^en fr°m Te^i [25]. Effects of energy and mass transfer on each other were taken into account in forming the energy equations. On the other hand the axial transfer of heat was neglected in this formulation. Physical properties taking place in the equations for the con servation of momentum, mass and heat, are dependent on temperature and concentration. Furthermore the system of equations is nonlinear. In the formulation of equations for the flow field, diffusion and energy nondimensional values of density were defined. Boundary conditions were defined in order to solve the system of equations. Further studies on the activation energy led to the intro duction of the latter as a parameter into the equation system. This however has rendered the equation system non-solvable. As shall be explained later, in order to obtain a specific solution of the equation system, the activation energy had to be excluded from the equation system. XIIIn other studies made up to date, concentrations of reactants were restricted to low values and the reactor was taken to be in an isothermal state. Thus by holding the density and other physical cha racteristics constant, the transfer of mass was expressed by a single equation and the activation energy in the boundary conditions was eliminated. Since the heat of reaction released had a small value, temperature in the whole reactor remained constant. Such studies of isothermal nature have not been able to serve any practical use except the revelation of the chemical conversion of the diffusion. Under cer tain circumstances contradictions in the reaction kinetics were observed. Physical properties related to gas mixtures that are considered in the mathematical model, are taken as dependent on temperature and concentration. In addition to above additions related to the consi deration of temperature variation in the model reactions, reaction enthalpies, equilibrium and chemical conversions have been defined. Equation systems for flow, energy and mass transfer in the reactor ((3,4,13).....(3,4,17)) are nonlinear. Due to the fact that the physical characteristics have been considered in detail, solution by classical methods is not possible. For this reason the finite difference method was used in the solution. Consequently the nonlinear terms in the equation system were lineariarized. The finite difference formulas thus obtained were solved iteratively. In the numerical solution, the unknown being calculated discretely, the axial and radial distances are defined by Ax* and Ar*, i and j indices in the finite difference formulas denote nodal points in the axial and radial directions respec tively. For values obtained in each step of iteration, relative error criterion wasvdefined as follows: -fi£2-S«r* ! A stability factor, CT, equal to 0.75 was used in the calcula tions. Examination of the numerical solution show that during the course of the reaction velocity rises connected with a pressure drop are observed, especially due to the rise of temperature and drop in density. Rise of temperature also affects the transport phenomena directly, since folloving a rise in temperature, values of `?£, X£, D/c and D* increase. In anadiabatic reactor, the maximum temperature obtained at the end of reaction is known as the adiabatic end tem perature: T*. = 1 + Y..H* ad, co A0 XIIIRise of the reactant concentration increases the Y. value. A0 The sole experimental data for ethylene hydrogenation model in the adiabatic tubular reactors are those given by Renken [16] and those determining the chemical conversion by the logarithmic Sherwood number. The theoretical values calculated from the data of Renken are given in figure 16. Renken made his measurements at a tempera ture of 457 K. The theoretical curve was calculated by taking the entry temperature of 400 K. Therefore, although the theoretical curve remains slightly above the test data, a perfect conformity has been obtained. Due to the fact that the reactant concentration above is high, the release of heat in the reactor, the rise of temperature, activation energy appearing in the boundary conditions render the solution of the problem impossible. For this reason, in the present studies, an average temperature was defined as follows: 2 o ad,oo and an average Domkohler number was defined as: Da k(T)R.?Q.frT» /b*£ab0. Therefore, activation energy was excluded from the boundary conditions and new boundary conditions were adapted by taking this average Damköhler number as parameter. The following equation can be written which expresses the relationship between the Damköhler number DaQ and the average Damköhler number Dâ: Da = Da0exp (E£Ö-l/(0,5(l+T*doo )))) Approximate solution was obtained by solving the finite diffe rence equations iteratively. This solution was found on the basis of flow, energy and mass transfer equations, under the boundary condi tions given above. XIVSince the average Damköhler nuber Da is the only parameter in the approximate mathematical solution, the chemical conversion diagrams belonging to any exothermic catalytic gas reaction can be prepared by solving the system of equations for various values of Da. By means of these diagrams the Ua values for the measured values of conversion corresponding to the average temperature, T defined as: T = -4- (T +T. ) 2 x o ad,oo' are obtained. Thus from these values the activation energy and the frequency factor for the concerning reaction can be determined. Also in this study, chemical conversion diagrams for the reac tions of propylene and butylene hydrogenation are given with the approximate method of solution. XV