STUDY OF CHEMICAL PROCESS STRUCTURES FOR PROCESS SYNTHESIS
Hiroshi OAKI and Masaru ISHIDA Research Laboratory of Resources Utilization, Tokyo Institute of Technology, Yokohama227
Whenthermodynamic characteristics of processes are represented by a vector on the (JH, TqJS) diagram, the processes may be classified into six types: heating, separation, refrigeration, heat source, mixing, and refrigerant. Based on this classification, which is quite appropriate to process synthesis, the analogy between chemical reactions and physical operations is discussed. Since a chemical process system is considered to be an isolated system, the criterion for those processes to constitute a process system is examined and a new criterion based on the dissipation factor, D=T0JS/JH9 is proposed. It is shown that there are only six basic patterns for the combination of processes to makeup a process system. Whenan endergonicprocess and an exergonic one constitute a process systemand the former process is carried out with the help of the latter, the exergy transformation between these two processes becomes an important factor. The concept of the ideality index is introduced and the relationship between this ideality index and the dissipation factor Dis discussed.
state to another2\ we mayevaluate the changes in Introduction enthalpy, AH, and entropy, AS, for each process. In chemical engineering, the process has usually Then we may describe thermodynamic character- been classified according to the type of equipment or istics of the process by a vector on the {AH, TQAS) operations such as heat generation, heat transfer, diagram shown in Fig. 1. distillation, absorption, extraction, and so on8>11). In this diagram, the enthalpy change is chosen as Such classification is suitable for equipment design abscissa and the entropy change multiplied by the calculations. However, based on this classification, ambient temperature To is selected as ordinate. Then many kinds of chemical reactions have been cate- the axis for Ae=0is represented by the oblique line gorized into only one group. given by AH=T0AS, since the exergy function e is In the previous paper7\ the authors proposed a new defined as methodto analyze a chemical process system from the e=H-T0S (1) viewpoint of exergy transformation between the target Therefore, we may divide the plane shown in Fig. 1 process and coupled processes such as exergy donors, into six regions by these three lines, AH=0(ordinate), exergy acceptors, accelerators, and mediators. It AS=0 (abscissa), and As=0 (oblique line). As will was shownthat there maybe several patterns for coupl- be explained later, these six regions may be called ing between the target and the coupled processes. Fromthat discussion, it was concluded that such clas- heating, separation, refrigeration, heat source, mixing, sification of processes based on type of equipments is and refrigerant types. not suitable for the energy analysis or synthesis of processes. The purpose of this paper is to classify processes into six types from the viewpoint of thermodynamics. Based on such classification, the criterion for several processes to constitute a process system is discussed. Finally, the efficiency of the exergy transformation in a basic binary process system is obtained. 1. Classification of Processes on (AH, TQAS) Plane Since a process is the transition ofa system from one Received April 10, 1981. Correspondence concerning this article should be addressed to H. Oaki. Fig. 1 Six types of processes on (AH, T0JS) diagram
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52 JOURNAL OF CHEMICAL ENGINEERING OF JAPAN The exergy increase of the above separation process is almost equal to that of the decomposition of a mole of methane or the refrigeration of 16 moles of nitrogen from 298 K to 100K, as shown in Fig. 3. However, the methodsto realize these endergonic processes are quite different from each other, as will be discussed in detail in the next section. Therefore, the process of which the vector is located in region (2) in Fig. 1 is called separation type. 2) Mixing Since mixing is the reverse of separa- tion, the changes in enthalpy and entropy are usually Fig. 3 Three kinds of endergonic processes with negative and positive, respectively. Therefore, its almost equivalent amount of As vector (AH, T0AS) appears in region (5) in Fig. 1. Hence, this region is called mixing type. 1. 4 Chemical reaction To perform detailed energy analyses for chemical reactions, information about concentrations of both reactants and products are required. Then the changes in enthalpy, entropy, exergy, and the dissipation factor for reactions can be calculated. For primary discussions for process synthesis, however, the stand- Fig. 4 Examples of endergonic reactions ard dissipation factor D°, defined by the following equation, may be utilized. D°=T0AS0/AH (ll) where S° is the entropy of each componentunder unit pressure. Figure 4 shows the vectors on the (AH, T0AS) diagram for several endergonic reactions based on thermodynamic data compiled in the literatures1>9). Figure 5 shows those for exergonic reactions. Since the vector of the reverse reaction appears in the op- posite direction, all six types can be observed in chemi- cal reactions. The reactants of exergonic reactions with negative or small positive values of D such as ATP, shown in Fig. 5, have been called high-energy compounds5 }. Figure 6 shows the effect of temperature on the value of dissipation factor D. It is found that D for chemi- cal reactions is almost constant over a wide range of temperature. Whenit is assumed to be constant, it becomes the reciprocal of the dimensionless tempera- ture at which the change in Gibbs free energy AG becomeszero as follows. D= T0AS/AH= T0/Teq (12) where AG&t Teq=AHKt req-7VfSat Te(l=0 (13)
Hence, from the value of D, one may estimate the Fig. 6 Dissipation factor diagram temperature ranges in which the reaction mayproceed. This may become an important advantage of D, mixing, chemical reactions, and so on and which especially for reaction syntheses. satisfies the following two conditions. 2. Criteria for a Process System JHi=0 (First law of thermodynamics) (14) Let us consider a process system which contains several processes, such as heat exchange, separation, z/aS^O (Second law of thermodynamics) (15) 2 VOL. 15 NO. 1 1982 53 Fig. 8 Synthesis of process of mixing type from two processes of different types a and b -(Ae1+Ae2)=TQ(AS1+AS2) =(D1-D2)AH1^0 (19) Whenprocess 1 is of heating, separation, or ref- rigerant type, for example, AHis positive and the following equation becomes the necessary condition Fig. 7 Six combinations for basic binary process systems for the process 1 to proceed. composedof processes 1 and 2 A^A for AHt>0 (20) The increase in entropy is caused by irreversible On the other hand, when process 1 is of refrigeration, processes in the system. heat source, or mixing type, AHis negative and we From Eqs. (14) and (15), we obtain have A^A for AHx<0 (21) S Jei=i=l t i=l VHt-T^S^-To t i=lJfi^O (16) The equality in Eqs. (20) and (21) holds when the This equation means that the summation of the exergy system is at equilibrium. change Ae over all processes in a process system is A=A (at equilibrium) (22) zero or negative. Consequently, Eq. (20) or (21) is used to judge However, a certain process, say process 1, in this whether the basic process system may hold. process system mayhave a positive change in exergy as follows : Figure 7 shows that there are only six combinations for processes 1 and 2 to satisfy that criterion. Four j£1=JH1- T0JS1>0 (for an endergonic process) of themare combinations of an endergonic process 1 To drive this endergonic process 1, the process system and an exergonic process 2, and the other two are must have other exergonic processes which supply a combinations of two exergonic processes. sufficient amount of exergy to process 1. Let us examine the characteristics of these combina- Not only chemical processes but also heat exchange tions. or separation processes may be considered to consti- 1) Heating type and heat source type Heat ex- tute a process system whenappropriate heat sources or change is a typical example. And from Fig. 2 and Eq. sinks and reservoirs for reactants and products are (4), it is found that Eq. (20) or (21) gives. included in it. Jin for process 1
54 JOURNAL OF CHEMICAL ENGINEERING OF JAPAN in this manner the energy and exergy transformation resultant process has the following properties. for such chemical reactions is quite analogous to that AHa+i=AHa+ AHh (25) for heat exchange operations. _ AHaDa+ AHhDh When the dissipation factor for an endergonic re- d^ = ~^+ Ih^~ (26) action approaches zero, for example Z>=0.083 for 4) Refrigeration type and refrigerant type This the decomposition of FeOto iron and oxygen, a heat source at quite high temperature is required. Then combination shown in (IV) in Fig. 7 is seen when a substance is refrigerated by using a refrigerant. In we may combine it with an exergonic reaction of which dissipation factor is smaller than that of the ender- this case cooling the substance is a process of refrigera- gonic reaction. When the reaction H2+0.5O2-> tion, and the refrigerant acts as a process of refrigerant H2O (D=0.055) is combined, the following overall type. reaction is obtained. 5) Refrigerant type and heat source or mixing type These are combinations of two exergonic processes. FeO+H2-+Fe+H2O The total entropy increase is large, as seen in Fig. 7(V) 2) Heating type and mixing type The reaction of or (VI). The latter combination is often utilized in heating type may also be combined with that of mix- increase the rate of the process, for example in the ing type. For the previous example, we maycombine case when a refrigerant below the ambient tempera- also the reaction C+0.5 O2-+CO (Z>=-0.242), re- ture To is used to quickly cool a substance at high tem- sulting in perature. FeO+C-*Fe+CO 3. Thermodynamic Efficiency Another famous example is the hydrolysis of ATP, The scheme of exergy flow in the basic binary which is often used as an exergonic rection in biochem- istry. process system with an endergonic process and an exergonic one discussed in the previous section indi- 3) Separationtype and mixingtype Itis to be noted that the separation type has only one combination, cates that the exergy loss in the latter process is utilized to carry out the former one. Hence, the ratio of the namely with the mixing type. It is known that the exergy gain in endergonic process 1 to the exergy active transport of various kinds of ions maybe achiev- ed by the help of the hydrolysis of ATP of mixing loss in exergonic process 2 is a kind of thermodynamic type10). Although the separation cannot take place by efficiency with respect to the exergy transformation. a process of heat source type alone, we maysynthesize Such efficiency for a process system was called ideality index ^z in the previous paper7). a process of mixing type by combining two vectors of __4ei=_AH.-TJS, 1-A ni, different types. Someexamples are shown in Fig. 8. Vl~ Ae2 AH2-T,AS2~\-~D2 {} For distillation, for example, the type of process in the reboiler is heat source (vector i-a in Fig. 8), and that Figure 9 shows the relationship between this ideality in the condenser is heating (i-b). Addition of these index and the dissipation factor D. As shown in re- two vectors results in a vector of mixing type. The gion (I) in Fig. 9, the ideality index becomes unity active transport in an artificial membranecaused by when the dissipation factor of endergonic process 1 temperature difference^ is also explained by the vec- is equal to that of exergonic process 2. For a heat tors (i-a) and (i-b). Other examples are addition of exchange operation, for example, this situation can be the vector of refrigerant type (ii-a in Fig. 8) and that achieved only when the heat exchange area is infinitely of refrigeration type (ii-b) or of the vector on the large. Such operation is called quasi-equilibrium- abscissa (iii-a, an extreme case of heat source type) state or reversible operation. and of heating type (iii-b). The former may be It is to be noted in this region (I) that the ideality observed for the case of low-temperature separation index becomes nearly equal to unity for very small and the latter for electrodialysis or reverse osmosis. values ofDu even when D±is not equal to D2. When two processes a and b are combined, the On the other hand, the ideality index in region (II)
VOL. 15 NO. 1 1982 55 as TJTln for thermal processes, T0/[(cp/cm)Tln\ for polytropic processes, and T0/Te(l for chemical reac- tions. 3) Based on D, a new criterionforprocesses to con- stitute a process system is derived. It maybe applied not only to isothermal processes but also to noniso- thermal ones. It is shown that there are only six Fig. 10 (AH, T0JS) diagram for reduction of iron basic patterns for such combination of processes. oxide by carbon 4) The efficiency of exergy transformation in the basic binary process system is discussed. never attains unity and approaches zero whenA/A Nomenclature approaches 0, i. e., A-åº-°°- Also in region (III) it decreases as the value of A/A becomes zero, i.e., cm = polytropic molar heat [kJ/K - mol] A-»-°°. cp = specific heat at constant pressure [kJ/K - mol] cv = specific heat at constant volume [kJ/K - mol] Region (IV) is the case when a process of refrigera- D = dissipation factor= T0JS/JH [-] tion type is combined with that of refrigerant type. G = Gibbs free energy [kJ] However, the ideality index in this region is quite dif- H =enthalpy [kJ] ferent from that in region (I). This difference is caused m = polytropic exponent [-] P = pressure [atm] by the importance of the entropy change at low tem- R = gasconstant [kJ/K-mol] peratures. S = entropy [kJ/K] As an example, let us calculate the ideality index for T = temperature [K] the reduction of wustite by carbon. Whenthis reac- TQ = temperature of surroundings [K] tion takes place at 1400K, 99.4kJ of heat must be supplied, and Fig. 10 shows the vectors for this heat e = exergy function [kJ] y = adiabatic expansion exponent [-] donor, the reaction donor, and the target reaction. r]r = ideality index [-] Also, the vector for the assembled donor, which is the vector sum of the reaction donor and the heat donor, Literature Cited and that for the whole process system are represented. 1) Brain, I. and O. Knacke: "Thermochemical Properties Since the dissipation factors for the target reaction and of Inorganic Substance", Springer-Verlag (1 973). the assembled donor at HOOKare A=0.187 and 2) Darken, L. S. and R. W. Gurry: "Physical Chemistry of A=-0.0214, respectively, the ideality index for this Metals", McGraw-Hill (1953). 3) Geidt, W. H.: "Thermophysics", Litton Educational process system, which belongs to region (II) in Fig. 9, Publishing, Inc. (1971). is given as ?7=(l-A)/(l-A)=(l-0.187)/(l+ 4) Kojima, K. : "Thermodynamics for Chemical Engineers" 0.0214)=0.796. An ideal process system with rjI=\ (in Japanese), Baifuukan, Tokyo (1968). corresponds to the condition that the vector for the 5) Lehninger, A. L.: "Bioenergetics", 2nd ed., Benjamin whole process system becomes zero vector. (1971). 6) Oaki, H. and M. Ishida: Membrane, 5, 371 (1980). Conclusion 7) Oaki, H., M. Ishida, and T. Ikawa: /. Japan Petrol. Inst. 24, 36 (1981). 1) Processes are classified into six types-heating, 8) Perry, R. H. and C. H. Chilton: "Chemical Engineers' separation, refrigeration, heat source, mixing, and re- Handbook", 5th ed., McGraw-Hill (1973). frigerant-from the viewpoint of thermodynamics, 9) Reid, R. C, J. M. Prausnitz, and T. K. Sherwood: "The Properties of Gases and Liquids", McGraw-Hill (1977). and the analogy between chemical reactions and physi- 10) Stryer, L. : "Biochemistry", Freeman & Co. (1975). cal operations is discussed. ll) The Soc. of Chem. Engrs., Japan: "Chemical Engineers' 2) The dissipation factor D(=T0JS/JH) is given Handbook" (in Japanese), 4th ed., Maruzen, Tokyo (1978).
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