Structured Process Energy-Exergy-Flow Diagram and Ideality Index for Analysis of Energy Transformation in Chemical Processes (Part 1) Application to Unit Processes Hiroshi OAKI*, Masaru ISHIDA* and Tsuneo IKAWA* A new diagram called structured process energy-exergy-flow diagram (SPEED) is proposed to systematically analyze the structure of energy flow in chemical processes and to design the process structures effectively. In the SPEED, process components are classified into five categories; target process, mediator, energy donor, accelerator, and energy acceptor. The target process is placed at the top of the SPEED and the other four are distinguished from each other by dotted, solid, double, and ripple lines, respectively. Several illustrative examples of SPEEDs are given. The ideality index is also defined. It is calculated based on the SPEED and it indicates the efficiency of exergy transformation in chemical process. It is a powerful index for identifying the portion where energy is wasted and for improving the process structure. It is found that the ideality index becomes unity when the process is performed reversibly under equilibrium conditions. 1. Introduction Analyses of energy flow in chemical processes have been based mainly on the first law of thermodynamics. Recently, many pioneer investigations about exergy have been made based on the second law of thermodynamics, and many methods for analysis of energy losses in the processes have been proposed.1)-12) However, most of those methods are still not adequate to systematically analyze the structure of energy flow and to design complicated chemical processes effectively. The object of most chemical processes is to make a target process, which can not proceed spontaneously in the natural environments, but which takes place by some artificial means. One of such means is to couple this target process with other processes which may proceed spontaneously. Another is to establish some artificial environment, for example, high temperature or high pressure in a reactor. To prepare such artificial environment, various processes which can proceed spontaneously are often coupled. From this concept, chemical processes are found to have a hierarchy Received April 25, 1980. * Research Laboratory of Resources Utilization, Tokyo Midori- Institute of Technology (4259, Nagatsuta-cho, ku, Yokohama 227) structure composed of the target process and energy donors. In this paper, a structured process energy-exergy-flow diagram is proposed to clarify this hierarchy structure of petrochemical or chemical processes. It consists of the target process, mediators, energy donors, accelerators, and energy acceptors. Furthermore, the ideality index is defined as the ratio of the increase in exergy in the target process to the decrease in exergy in other coupled processes and it indicates the efficiency of exergy transformation in chemical processes. 2. Structured Process Energy-Exergy-Flow Diagram (SPEED) A chemical process is considered to be an assembly of chemical reactions, separation, mixing, heat exchange, and others. The transfer of energy in each process will be discussed from the viewpoint of conjugation between the target process and energy donors. 2.1 Chemical Reaction Biosynthesis of gultamine from gultamic acid and ammonia is carried out by ATP as an energy carrier as follows: As is well known, this reaction composes of two conjugate reactions, as shown in Fig. 1 (a). The
37 nary copula, the above reaction may be decomposed to a target reaction and a donor, as shown in Fig. 1 (b). Although simple molecules are usually chosen as copulas in this study, functional groups may also be selected as follows: such description as Eq. (3) or (4) is adopted, energy calculations for functional groups are required and they will be discussed elsewhere. The amination of methane and reduction of an iron oxide whose overall reactions are represented in Eqs. (5) and (6), may also be decomposed to the target process and the energy donor, as shown in Fig. 1 (c) and (d), respectively. Since the donor plays the role of supplying energy to the target reaction, we may have several kinds of choices. For example, the following reaction may be selected as the donor for the amination of methane shown in Fig. 1 (c). Fig. 1 SPEED for Chemical Reactions with Donors reaction over the solid line in Fig. 1 (a) is the target endergonic reaction. On the other hand, the reaction immediately below the line is exergonic and it donates energy to the target reaction. The water molecule as a copula, connects the target reaction and the energy donor. Hence, such conjugate reactions may be represented by a general formula shown in Scheme I (i) or (ii) in Fig. 1. In the former notation, the target process is placed at top and the subsidiary process is written below it. Hence, the rank of each process in the hierarchy structure of the chemical process system is represented by the level of the row. In the latter notation, it is denoted by the tab shift. Such coupling of conjugate reactions may be observed in many processes in the petrochemical and chemical industries. The following oxidative dehydrogenation of n-butane is one of these examples in which 1-butene is the target product. When hydrogen molecule is chosen as an imagi- Also, the same reaction may be used as the donor for the reduction of the iron oxide represented in Fig. 1 (d). Synthesis of methylamine from methane shown in Fig. 1 (c) is now being carried out by successive reactions. In such a case, the choice of an intermediate product is quite important. Its choice will be discussed in detail in Part II. So far, the transfer of free energy has been discussed. On the other hand, the conjugation of enthalpy may also be seen in many chemical processes. An example is the partial oxidation of methane at 1,500K. This reaction is decomposed to the target and the donor, as shown in Fig. 1 (e). Heat and light are also important energy donors. An example of light is the decomposition of silver bromide, as shown in Fig. 1 (f). In the above examples, the target reaction is coupled directly with the donor. However, some target reactions may progress spontaneously, if appropriate conditions, for example, high temperature and high pressure, are satisfied. We call these conditions, or artificial environment in the reactor the mediator. Since donors are often required to satisfy such conditions, the process structure of
Fig. 3 SPEED for a Heat Exchanger Fig. 2 SPEED for Chemical Reactions with Mediators these reactions may be represented by Scheme II (i) or (ii) in Fig. 2. The diagram to represent the process structure according to Scheme I or II will be called the structured process energy-exergyflow diagram. We abbreviate it as SPEED in later sections. An example of a process with a mediator is the electrolysis of water to hydrogen and oxygen effected by the electric potential difference between the electrodes. In this case, the potential gradient is the mediator. We will draw a dotted line above the mediator in the SPEED, as shown in Fig. 2 (a). The reaction of hydrogen and chlorine to form hydrogen chloride takes place by means of light, as shown in Fig. 2 (b). However, this reaction is exergonic and light plays the role of an accelerator to initiate the photochemical chain reaction. We will draw a double line over the accelerator light in the SPEED. Since the interrelations between the target reaction and other coupled processes are shown clearly, the SPEED is a convenient diagram for analyzing the energy flow in chemical processes and for summarizing their hierarchy structures. 2.2 Heat Exchanger The SPEED for a heat exchanger is shown in Fig. 3 (a). In this case, the increase in the temperature of a moles of fluid A from TA1 to TA2 is the target process, while the decrease in the temperature of 6 moles of the fluid B from TB1 to TB2 is the energy donor. On the other hand, cooling of a fluid below the ambient temperature To requires refrigeration. Its SPEED is shown in Fig. 3 (b). In many industrial processes, a coolant is used to decrease the temperature of the target fluid, say, is an exergonic process and it may proceed spontaneously. Hence the coolant is used as the accelerator to increase the cooling rate, as shown in Fig. 3 (c). 2.3 Separation Separation of mixtures is often performed by distillation, and its target process may be expressed as follows: where the braces denote the mixture of the fluids and nf and nd denote the molar flow rates of feed and distillate, respectively. Its SPEED is shown Fig. 4 SPEED for a Distillation Process
(i) T>T0 (ii) T<T0 (i) (ii) (i) T>T0 (ii) T<T0 (a) Donor (b) Accelerator (c) Acceptor Fig. 6 Flow of Enthalpy (Open Arrow), Free Energy (Dotted Arrow) and Exergy (Striped Arrow) for Donors, Accelerators, and Acceptors the maximum work obtained from the heat T (S- total work derived from the system is given by (H-Ho)-TO(S-So). This is equal to the exergy in Fig. 4. HEATING INPUT and REBOILING indicate that heat is required to raise the feed to a specified temperature and to evaporate it in the reboiler, and CONDENSING and COOLING TOP and BOTTOM PRODUCTs indicate that heat may be recovered by the energy acceptors in the condenser from both products. We will draw a ripple line for the acceptor in the SPEED. Other kinds of separation processes are also available. For desalination of brine, for example, processes for evaporation, reverse osmosis, and electro-dialysis are being studied. SPEEDs for those processes may be drawn, as shown in Fig. 5 (a) through (c). 3. Scheme of energy transformation Let's summarize the flows of enthalpy, free energy, and exergy. Fig. 6 (a) shows the energy flow from the donor. The open arrow shows the flow of enthalpy, H. Since enthalpy is conserved, the total amount of decrease in enthalpy in the donor will be transferred to the target process. Hence, the arrow for the enthalpy in Fig. 6 (a-i) has a constant width. The dotted arrow shows the flow of free energy, G. Since it is not conserved generally, only a certain quantity of the free energy loss of the donor will be transferred to the target process. This situation is described by changing the width of the arrow in Fig. 6 (a-i). Fig. 5 SPEED for Desalination Processes T(S-So), is derived by a reversible reaction, the heat T(S-So) is released from the system. Since is the exergy function defined by H-ToS. The change in the width of the striped arrow for the exergy in Fig. 6 (a-i) shows its dissipative nature. Fig. 6 (a-ii) shows the case when the fluid is refrigerated below the temperature of the environment, To. In this case, the arrows of both enthalpy and free energy are directed downward, while the arrow of the exergy is kept upward. Fig. 6 (b) shows the energy flow caused by an accelerator. Since the role of the accelerator is to increase the rate, the exergy transferred from the accelerator to the target process is usually negligible, as shown in Fig. 6 (b-i). In some cases such as cooling of a hot fluid by a coolant, the direction of exergy flow is reversed, as shown in Fig. 6 (b-ii), even if a substantial amount of mechanical work is required to produce the coolant. With respect to the acceptor, the exergy will be transferred from the main process above the ripple line to the exergy acceptor, as shown in Fig. 6 (c). The flow of enthalpy and free energy is directed downward for T>To, as shown in Fig. 6 (c-i), while upward for T<To, as shown in Fig. 6 c-ii). 4. Definition of Ideality Index The scheme of energy flow on the SPEED indicates that the exergy loss in the donor is utilized to carry out the target process. Hence, the ratio of exergy gain in the target process to exergy loss in the donor process is a kind of thermodynamic efficiency with respect to the exergy transformation. Since various kinds of efficiency are being defined, the accelerator and the acceptor are also taken defined as follows:
Fig. 8 SPEED for Reaction, Eq. (11) at a Constant Temperature Fig. 7 Ideality Index for a Heat Exchanger and a Chemical Reaction By separating chemical reactions into target reactions and donors, any complex chemical process may be analyzed systematically by the SPEED, and the ideality index may be calculated. When the process does not have any chemical reaction, this ideality index becomes equal to the thermodynamic efficiency or the effectiveness index defined in literature.5),7) Ideality indexes for industrial processes will be discussed in Part II. It is noteworthy to discuss the relationship between this ideality index and the degree of deviation from equilibrium. Two examples, a heat exchanger and a simple chemical reaction are considered. (Heat Exchanger) The ideality index for a heat exchanger is obtained as follows when we neglect the heat loss. where acpa is assumed to be equal to bcpb and TAln is the logarithmic mean temperature defined by TAln=(TA1-TA2)/ln(TA1/TA2). As shown in Fig. 7, the ideality index becomes unity when the mean temperature of fluid A is equal to that of fluid B. This situation can be achieved only when the area is infinitely large. However, when the mean temperature of fluid A is equal to the ambient temperature, the ideality index becomes zero. (Chemical Reaction) Let's consider the following type of reaction. The oxidative dehydrogenation of n-butane is an example of this type of reaction. When this endothermic reaction is performed at a constant temperature, T, we must supply heat. Hence, the SPEED for this process needs two donors, as shown in Fig. 8 (a). When the reaction is exothermic, an acceptor is substituted for a donor, as shown in Fig. 8 (b). Then, the ideality index is calculated as follows: each component in the feed to produce a mole of the target product C. The subscript 1 and 2, respectively, denote the inlet and the outlet of the reactor, and Pie is the partial pressure of the component i in equilibrium. In the above calculation, the activity of copula X is assumed to be unity. Equation (12) is quite similar to Eq. (10) for heat exchangers. Hence, Fig. 7 may be applied also for the chemical reaction when such imaginary temperatures as TTarget and TDonor are introduced. And, the ideality index becomes unity when the reaction takes place reversibly under equilibrium conditions.
41 5. Conclusions (1) The structured process energy-exergy-flow diagram (SPEED) is proposed for analysis of hierarchy structure of chemical processes from the viewpoint of exergy transformation. (2) SPEED consists of five kinds of process components; target, mediator, donor, accelerator, and acceptor. The target is placed at the top of SPEED and the other four are distinguished from each other by dotted, solid, double, and ripple lines. (3) The ideality index is defined as the efficiency of exergy transformation in a chemical process. It is calculated by a simple algorithm based on the SPEED. (4) The ideality index becomes unity when each process is carried out reversibly under equilibrium conditions. References 1) Matsuyama, T., Kagaku Kikai, 14, 83 (1950). 2) Keenan, J. H., British J. of App. Physics., 2, 184, (1951). 3) Uraguchi, Y., Kagaku Kogaku, 19, 236 (1955). 4) Denbigh, K. G., Chem. Eng. Sci., 6, 1, (1956). 5) Kojima, K., "Thermodynamics for chemical engineers" Baifuukan, Tokyo (1968). 6) King, C. J., "Separation Processes", McGraw Hill, N. Y. (1971). 7) Riekert, L., Chem. Eng. Sci., 29, 1613, (1973). 8) Nobusawa, T., Nenryo oyobi Nensho, 41, 225 (1974). 9) Reistad, G. M., Trans. A.S.M.E., Ser. A. 97, 429, (1975). 10) Shiroko, K., Itoh, J., Kagaku Kogaku, 41, 464, (1977). 11) Ikawa, T., Kagaku To Kogyo, 33, 160 (1980). 12) Kameyama, H., Yoshida, K., Kagaku Kogaku, 43, 390, (1979).
Keywords Exergy, Energy transformation, Process analysis, Energy balance, Efficiency