Principles Of Unit Operations By Foust
Rapheal Charlton
that to which the mercury stream is lowered as it leavesthe contacting equipment, as indicated in Figure 1.The counterflow principle is used in many chemical-engineering operations in order to permit greater transfer of a property than would be indicated merely by theattainment of a single equilibrium between the leaving streams. Continuous and Batch Operation. In the majority ofchemical processing operations, it is more economical tomaintain continuous and steady operation of equipment,with a minimum of disturbances and shutdowns. This isnot always practical in some small-scale operations, inoperations where extremely corrosive conditions forcefrequent repairs, and in others for various specificreasons. Because of the greater productivity of con-tinuously operating equipment and the resultant lowerunit cost, it is usually advantageous to operate equipmentcontinuously. Thill means that time is not a variable inthe analysis of such a process, except during the ratherbrief start-up and shutdown periods. The time rate oftransfer or of reaction is important in fixing the necessarysize and capacity of equipment, but the performance isexpected to be the same today, tomorrow, or next yearif the operating conditions remain the same. Conditionsare not constant throughout a system at any time, butthose at a particular point are constant with time. When small quantities of material are to be processed,it is often more convenient to charge the entire quantity of material to the equipment, process it in place, andremove the products. This is called a batch operation. An operation which is variant with time is spoken of as a transient or unsteady state, in contrast with that spoken of as steady state, in which conditions are invariant with time. The quenching of a steel part for heat treating and the freezing of ice cubes in a domestic refrigerator are illustrations of unsteady-state operations. In batch operations, almost the entire cycle is a start-up transient and a shutdown transient. In a continuous operation, the time during which the start-up transient exists may be extremely small in comparison with the steady-state operation. Analysis of transient or batch operations is usually more complex than in steady-state operation. Because of the greatersim- plicity and the wide occurrence throughout chemical processing of steady-state operations, the introductory treatment is in terms of conditions which do not vary with time. Analysis of a transient operation is different from the steady state only in the introduction of the additional variable of time. This variable complicates the analysis but does not fundamentally change it.
of the material being operated upon and of other charac-teristics of the particular system. In the design of aprQcess, each step to be used can be studied individuallyif the steps are recognized. Some of the steps arechemical reactions, whereas others are physical changes.The versatility of chemical engineering originates intraining to the practice of breakin up a complex process into individual physical steps, called unit operations, andinto the chemical reactions. The unit-operations con-cept in chemical engineering is based on the philO"- sophy that the widely yarying sequences of steps can be reduced to simple operations or reactions, which are identical in fundamentals regardless of the material being processed. This principle, which became obvious to the pioneers during the development of the American chemical industry, was first clearly presented by A. D. Little in 1915:
"Any chemical process, on whatever scale conducted,may be resolved into a coordinated series of what may betermed 'unit actions,' as pulverizing, mixing, heating, roasting,.,absorbing, condensing, lixiviating, precipitating, crystallizing,-.....filtering, dissolving, electrolyzing and so on. The number ofthese basic unit operations is not very large and relativelyfew of them are involved in any particular process. Thecomplexity of chemical engineering results from the varietyof conditions as to temperature, pressure, etc., under whichthe unit actions must be carried out in different processesand from the limitations as to materials of construction anddesign of apparatus imposed by the physical and chemicalcharacter of the reacting substances." (2)
The original listing of the unit operations quotedabove names twelve actions, not all of which are con-sidered unit 0eerations. Additional ones have beendesignated since then, at a modest rate over the years butrecently at an accelerating rate. Fluid flow, heat transfer,distillation, humidification, gas absorption, sedimenta-tion, classification, agitation, and centrifugation havelong been recognized. In recent years ion exchange,adsorption, gaseous diffusion, fluidization, thermaldiffusion, hypersorption, chromatography, and othershave also been proposed for designation as unit operations.In general the term unit operatiolls has been restricted ,to those operations in which the changes are essentiallyphysical. This is not universally true, becaus@'the termgas absorption is used appropriately for the operationof removing one gas from a mixture whether the removalis accomplished by physical solution or by chemicalreaction with the solvent. Very frequently chemicalchanges occur in a material being distilled or heated.In such cases the physical operation is the primaryconcern, and, if a chemical change occurs simultaneously,it is usually handled by a modification of the physicalproperties of the material.The typical chemical manufacturing operation involvesa few chemical steps which are probably straightforwardand well understood. Rather extensive equipment and
(; PRINCIPLES OF UNIT OPERATIONSfrequently impossible to formulate the boundary condi-tions for solution of a mathematical expression inmanageable terms. Each of the three modes of grouping could be used asa basis. The physical model of the fundamental opera-tion is the most satisfactory approach and is used in thispresentation. Wherever possible, the physical model isdescribed mathematically, and the performance is ex-pressed in mathematical relations derived from thefundamental principles. This formulation gives the bestbasis for understanding and refining those operations inwhich the art is ahead of theory. This is true in spiteof the fact that the models are oversimplified and thatthe mathematical formulation of the behavior of themodel cannot be transposed perfectly into an expressionof the behavior of the prototype. It should be obvious that there is no universal criteriondictating a particular choice of method of analysis andthat all contributing factors should be recognized indeciding upon a particular mode. Any groupingrequires some arbitrary choice and always leaves one withsome of the operations which fit poorly into the generalscheme. Such operations must be studied individually.Two Major Physical Models. One widely applicablemodel for unit operations is a device in which twostreams, or phases, are brought together, allowed toreach equilibrium, then separated and withdrawn. Sinceit is assumed that the leaving streams are at equilibrium,this model is called an equilibrium stage. Evaluation ofthe changes in the streams which must be accomplishedto attain equilibrium establishes a measure of ultimateperformance. Real equipment is evaluated by expressingthe changes accomplished in it as a fraction or percentageof the changes that would occur in an equilibrium stage.In another possible model for transfer of a propertybetween two streams we visualize the carriers of theproperty, evaluate their }lumber and rate of migration,and arrive at an expression of the rate of transfer betweenthe two streams in continuous contact. This rate oftransfer multiplied by the time of contact yields anexpression for the amount of transfer accomplished.The equilibrium-stage model may be expressed mathe-matically in a finite-difference equation relating enteringconcentrations of any property with the equilibriumconcentrations of the property in the leaving streams.Graphical techniques frequently can be used moreconveniently than the finite-difference equation; Themathematical expression for the rate-of-transfer modelis a differential equation which can sometimes beintegrated rigorously but more frequently must behandled in terms of average conditions. Since a largenumber of chemical processing operations are actuallycarried out either stagewise or in continuous contact,these two models are widely applicable for the analysisof unit operations.
Rate Operations. The unit operations involving::wro1Jllr... contacting depend upon the rate of transfer,MiJJ!LI! therefore called rate operations. The transfer ofill! a. number of properties of a material-such ascal, magnetic, thermal, mass, and momentum:::r"'l:L-:entrations-follows the same basic mathematical!:"'I:;:rr::ssion of rate of transfer as a function of concen-1r:Xl0n gradient,(1)
Since chemical substances seldom fit nice mathematicalequations and since chemical equilibrium is constantlyupsetting neat formulations of boundary conditions whichwould permit rigorous solutions of EquatIon 1, variousaverages and approximations must be used in arrivingat an answer in an economical length of time. Thesimplifications usually approach Equation 1 muchmore closely than the rigorous diffusion equation.For the rate operations, analysis must be based uponthe driving force causing a change, the time during whicha driving force is allowed to act, and the quantity ofmaterial upon which it acts. The diffusion equationabove expreses the transient behavior of a large numberof properties under the influence of a driving force fortransport of the property. In chemical engineering,mass, momentum, and thermal energy are the three pro-perties whose transport is the most frequently involved.As mentioned above, it is universal that these three pro-perties, along with a number of others in which chemicalengineers are less frequently concerned, tend to flowfrom. regions of high concentration to regions of lowconcentration. Accurate prediction of the amolnlt ofthe property which flows from a donor region (s(lurce)to a receiver region (sink) can be made if the drivingforce, the area of the path, and the unit resistivity of thepath (the proportionality constant used in Equation 1)are accurately known. Throughout the study of therate operations, the importance of a clear understandingof the meaning of concentration cannot be overstressed.In every case, the concentration expresses the amount ofproperty per unit volume of the phase being processed.The amount being transferred can usually be expressedin some absolute unit measuring that quantity such asBtu's, or pound moles. It can also be expressed interms of the decrease in concentration of the propertyin a known amount of phase having a known capacity forthis property. For example, a quantity of energy leavinga system as heat can be expressed in terms of the numt)erof Btu's or calories of energy. It can also be expressedin terms of the decreae of temperature of a known amountof the phase. These generalizations will become moremeaningful as different operations are analyzed and thetransported quantities are expressed in terms of thevarious possible units. Since the basic principles of trans-port are identical for the three properties, an analysiswill be offered in completely general terms before specifi-cation of the particular property in specific operations.Unsteady-State Operation. The diffusion equation,Equation 1, is applicable to a change which is a functionof time.
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