Heat and Mass Transfer Christo Boyadjiev Maria Doichinova Boyan Boyadjiev Petya Popova-Krumova Modeling of Column Apparatus Processes Heat and Mass Transfer Series editors D. Mewes, Hannover, Germany F. Mayinger, München, Germany More information about this series at http://www.springer.com/series/4247 Christo Boyadjiev Maria Doichinova (cid:129) Boyan Boyadjiev Petya Popova-Krumova (cid:129) Modeling of Column Apparatus Processes 123 Christo Boyadjiev Boyan Boyadjiev Institute of Chemical Engineering (IChE) ChemEng Ltd. BulgarianAcademy of Sciences (BAS) Sofia Sofia Bulgaria Bulgaria PetyaPopova-Krumova Maria Doichinova Institute of Chemical Engineering (IChE) Institute of Chemical Engineering (IChE) BulgarianAcademy of Sciences (BAS) BulgarianAcademy of Sciences (BAS) Sofia Sofia Bulgaria Bulgaria ISSN 1860-4846 ISSN 1860-4854 (electronic) Heat andMassTransfer ISBN978-3-319-28257-2 ISBN978-3-319-28259-6 (eBook) DOI 10.1007/978-3-319-28259-6 LibraryofCongressControlNumber:2015959592 ©SpringerInternationalPublishingSwitzerland2016 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpart of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission orinformationstorageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilar methodologynowknownorhereafterdeveloped. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publicationdoesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfrom therelevantprotectivelawsandregulationsandthereforefreeforgeneraluse. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authorsortheeditorsgiveawarranty,expressorimplied,withrespecttothematerialcontainedhereinor foranyerrorsoromissionsthatmayhavebeenmade. Printedonacid-freepaper ThisSpringerimprintispublishedbySpringerNature TheregisteredcompanyisSpringerInternationalPublishingAGSwitzerland The mathematical model of a complex of elementary processes is a mathematical structure, where the mathematical operators are mathematical descriptions of the elementary processes. Preface The complex processes in the column apparatuses have a combination of hydro- dynamic processes, convective and diffusive mass (heat) transfer processes, and chemical reactions between the reagents (components of the phases). The fundamental problemin the column apparatuses modelingis a result ofthe complicated hydrodynamic behavior of the flows in the columns, and thus, the velocity distributions in the columns are unknown. The column apparatuses are possible to be modeled, using a new approach on the base of the physical approximations of the mechanics of continua, where the mathematicalpointisequivalenttoasmall(elementary)physicalvolume,whichis sufficiently small with respect to the apparatus volume, but at the same time suf- ficiently large with respect to the intermolecular volumes in the medium. The mathematical models of the processes in the column apparatuses, in the physicalapproximationsofthemechanicsofcontinua,willbethemassbalancesin thephasevolumes(phasepartsintheelementaryvolume),betweentheconvective mass transfer (as a result of the fluid motions), the diffusive mass transfer (as a result of the concentration gradients), and the volume mass sources (sinks) (as a result of chemical reactions or interphase mass transfer). In the case of balance between these three effects, the mass transfer processes are stationary or in the opposite case, the processes are non-stationary. Theseconvection–diffusion-typemodelspermittobemadeaqualitativeanalysis of the processes (models) for to be obtained the main, small, and slight physical effects(mathematicaloperators),andtoberejectedtheslighteffect(operator).Asa result, the process mechanism identification is possible to be made. These models permit to be determinate the mass transfer resistances in the gas and liquid phases and the optimal dispersion system finding in gas absorption (gas–liquid drops or liquid–gas bubbles). The convection–diffusion models are a base of the average concentrationmodels,whichallowaquantitativeanalysisoftheprocessesincolumn apparatuses. Theconvection–diffusionmodelsarepossibletobeusedforqualitativeanalysis only, because the velocity distribution functions are unknown and cannot be vii viii Preface obtained.Theproblemcanbeavoidedbytheaverageconcentrationmodels,where the average values of the velocity and concentration over the cross-sectional area of the column are used; that is, the medium elementary volume (in the physical approximationsofthemechanicsofcontinua)willbeequivalenttoasmallcylinder with a real radius and a height, which is sufficiently small with respect to the column height and at the same time sufficiently large with respect to the inter- molecular distances in the medium. The convection–diffusion models and average concentration models are used forthequalitativeandquantitativeanalysisoftheprocessesinsinglephase(simple and complex chemical reactions), two phase (absorption, adsorption, and catalytic processes), and three phase (two-phase absorbent processes and absorption– adsorption processes). In many cases, the computer modeling of the processes in column apparatuses, on the base of a new approach, using the convection–diffusion-type model and averageconcentration-typemodel,doesnotallowadirectuseoftheMATLAB.In these cases, it is necessary to create combinations of MATLAB with appropriate algorithms. Practically, the new type models are characterized by the presence of small parameters at the highest derivatives. As a result, the use of the conventional software for solving of the model differential equations is difficult. This difficulty may be eliminated by an appropriate combination of MATLAB and perturbations method. In the cases of countercurrent gas–liquid or liquid–liquid processes, the mass transfer process models are presented in two coordinates systems, because in one coordinatesystemoneoftheequationshasnotasolutionbyreasonofthenegative equationLaplacian value. Acombination ofan iterative algorithms and MATLAB must be used for the solutions of the equations set in different coordinate systems. Inthecasesofanon-stationaryadsorptioningas–solidsystems,thepresenceof mobile (gas) and immobile (solid) phases in the conditions of long-time processes leadstothenon-stationaryprocessintheimmobilephaseandstationaryprocessin themobilephase,practically.Asaresult,differentcoordinatesystemsmustbeused in the gas and solid phase models. A combination of a multi-steps algorithms and MATLABmustbeusedforthesolutionsoftheequationssetindifferentcoordinate systems. The solid fuel combustion in the thermal power plants, which use sulfur-rich fuels, poses the problem of sulfur dioxide removal from the waste gases. This problemiscomplicatedbythefactthatitisrequiredtopurifyhugeamountsofgas with low sulfur dioxide concentration. The huge gas amounts need big size appa- ratuses,whichispossibletobedecreasediftheremovalprocessrateismaximized. Theprocessintensificationisrealizedwithanewpatentintwo-zonecolumn,where the upper zone is physical absorption in a gas–liquid drops system (intensification of the gas phase mass transfer), the lower zone is a physical absorption in liquid– gas bubbles system (intensification of the liquid phase mass transfer), and the chemical reaction takes place in the column tank. Preface ix Theproblemofabsorbentregenerationissolvedinanewpatent,usingtwosteps process—physical absorption of sulfur dioxide by water and adsorption of sulfur dioxide from the water solution by synthetic anionite particles. The adsorbent regeneration is made by ammonium hydroxide solution. The obtained ammonium sulfite solution is used (after reaction with nitric acid) for concentrated sulfur dioxide and ammonium nitrate solution production. The purification of large amounts of waste gases from combustion plants used countercurrentabsorbers,wherethegasvelocity(asaresultandabsorbersdiameter too) is limited by the rate of the absorbent drops fall in an immobile gas medium. This disadvantage is avoided by a new patent, where cocurrent sulfur dioxide absorption is realized. TheIntroductionconcernslinearmasstransfertheory(modeltheories,boundary layertheory,andtwo-phaseboundarylayers),masstransferincountercurrentflows (velocity and concentration distribution, and comparison analysis), nonlinear mass transfer (influence on the hydrodynamics, boundary conditions, boundary layer theory, and Marangoni effect), interphase mass transfer resistances (film and boundary layer theories approximations), three-phase mass transfer processes (physical, hydrodynamic and interphase mass transfer models, absorption mecha- nism, and kinetics). Part I focuses on the convection–diffusion-type models for qualitative analysis of the column apparatuses processes. In Chap. 2 are presented one-phase chemical processes in column reactors (simple and complex chemical reaction kinetics), approximations of the model (short- and high-columns model, effect of the chemical reaction rate), effect of the radial non-uniformity of the velocity distri- bution (conversion degree, concentration distribution, influence of the velocity radialnon-uniformityshape,scaleeffect,backmasstransfermechanism),examples (effect of the tangential flow, simultaneous mass and heat transfer processes, cir- culation zones in column apparatuses, and mass transfer in one-phase countercur- rent flow). In Chap. 3 are presented the convection–diffusion-type models of two-phase processes (physical and chemical absorption, physical and chemical adsorption,andcatalyticprocessesinthecasesofphysicalandchemicaladsorption mechanism), examples (airlift reactors, airlift photo-bioreactor, and moisture adsorption). In Chap. 4 are presented models of three-phase processes in the cases of two-phase absorbent processes (physical and chemical absorption) and absorp- tion–adsorption processes (physical and chemical adsorption mechanism), PartIIaddressestheaverageconcentration-typemodelsforquantitativeanalysis of the column apparatuses processes. In Chap. 5 are presented the average concentration-type models of the column reactors in the cases of simple and complex chemical reactions (effect of the velocity radial non-uniformity, model parameters identification) and as an example the modeling of a non-isothermal chemical reactor. In Chap. 6 are presented the interphase mass transfer models ofthephysicalandchemicalabsorption,physicalandchemicaladsorption,catalytic processes in the cases of physical and chemical adsorption mechanism, and as examples airlift reactor modeling and moisture adsorption modeling. x Preface Part III addresses the calculation problems in the convection–diffusion-type modelsandaverageconcentration-typemodels.Chapter7presentstheperturbation method approach for the solution of the equations in the convection–diffusion models and average concentration models. Chapter 8 presents the solutions of two coordinate systems’ problems in the models of the countercurrent absorption pro- cesses. Chapter 9 presents the multi-steps modeling algorithms in the case of a long-time non-stationary adsorption process, when the interphase gas–solid mass transfer is stationary. Part IV concerns the models of the processes, which participate in different patents, related with the waste gas purification from sulfur dioxide in column apparatuses.Chapter10presentsthemodelingofabizonalabsorptionapparatusfor sulfur dioxide absorption by two-phase absorbent. Chapter 11 presents the pro- cesses modeling of an absorption–adsorption method for waste gas purification fromsulfurdioxide,wherethefirststepisaphysicalabsorptionofsulfurdioxideby water and the second step is a chemical adsorption of sulfur dioxide in the water solution by synthetic anionite. After the sulfur dioxide saturation of the synthetic anionite particles, the adsorbent regeneration is possible to be carried out by water solutionofammoniumhydroxide.Chapter12presentstheprocessesmodelingina cocurrent apparatus, where the gas velocity is 4–5 times greater than that of the countercurrent apparatus, which are used in the practice. Christo Boyadjiev Maria Doichinova Boyan Boyadjiev Petya Popova-Krumova