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Second-Law Analysis

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Second-Law Analysis Second-Law Analysis 9S.0 OBJECTIVES The first law of thermodynamics is widely used in design to make energy balances around equipment. Much less used are the entropy balances based on the second law of thermodynamics. Although the first law can determine energy transfer requirements in the form of heat and shaft work for specified changes to streams or batches of materials, it cannot even give a clue as to whether energy is being used efficiently. As shown in this chapter, calculations with the second law or a combined first and second law can determine energy efficiency. The calculations are difficult to do by hand, but are readily carried out with a process simulation program. When the second-law efficiency of a process is found to be low, a better process should be sought. The average second-law efficiency for chemical plants is in the range of only 20-25%. Therefore, chemical engineers need to spend more effort in improving energy efficiency. After studying this supplement, the reader should 1. Understand the limitations of the first law of thermodynamics. 2. Understand the usefulness of the second law and a combined statement of the first and second laws. 3. Be able to specify a system and surroundings for conducting a second-law analysis. 4. Be able to derive and apply a combined statement of the first and second laws for the determination of lost work or exergy. 5. Be able to determine the second-law efficiency of a process and pinpoint the major areas of inefficiency (lost work). 6. Understand the causes of lost work and how to remedy them. 7. Be able to use a process simulation program to perform a second-law analysis. 9S-1 9S.1 INTRODUCTION A chemical process uses physical and/or chemical operations to transform feed materials into products of different composition. Table 9S.1 lists the types of operations that are most widely used. Depending on the production rate and the operations used, the process is conducted batchwise, continuously, or cyclically. A continuous, heat-integrated process that illustrates several of the operations in Table 9S.1 is shown in Figure 9S.1, where benzene and a mixture of xylene isomers are produced by the disproportionation of toluene. The heart of the process is a fixed-bed catalytic reactor, R-1, where the main chemical change is the reaction 2C7H8 → C6H6 + C8H10 isomers Table 9S.1 Common Operations in Chemical Processing Operation Examples of Equipment Used Change in chemical species Reactor Separation of chemicals Distillation, absorption, liquid-liquid extraction Separation of phases Settler Pressure change Pump, compressor, valve, turbine, expander Temperature or phase change Heat exchanger, condenser Mixing Agitated vessel, in-line mixer Dividing Pipe tee Size enlargement of solids Pellet mill Size reduction of solids Jaw crusher Separation of solids by size Screen This reaction is conducted in the presence of hydrogen to minimize the undesirable formation of coke by condensation reactions. However, other undesirable side reactions such as C7H8 + H2 → C6H6 + CH4 occur and produce light paraffins. Chemicals in the reactor effluent are separated from each other as follows. Hydrogen is recovered for recycle by partial condensation in exchanger E-2 with phase separation in flash drum D-1; light paraffin gases are removed in fractionator C-1; benzene is recovered and purified in fractionator C-2; and mixed xylenes are recovered and purified, and unreacted toluene is recovered for recycle in fractionator C-3. Compressors K-1 and K-2 bring 9S-2 Figure 9S.1 Process for disproportionation of toluene to benzene and xylenes. 9S-3 fresh hydrogen and recycled hydrogen, respectively, to reactor pressure. Pump P-1 brings fresh toluene to reactor pressure. Pumps P-2, P-3, and P-4 deliver reflux to fractionators C-1, C-2, and C-3, respectively. Pumps P-3 and P-6 deliver benzene and xylene products, respectively, to storage, and pump P-5 recycles toluene. Furnace F-1 uses the combustion of fuel oil with air to bring reactants to reactor temperature, after preheater E-1 has recovered a portion of the thermal energy in the reactor effluent. Cooling water is used in overhead condensers E-4, E-6, and E-9, and steam is used in reboilers E-5, E-7, and E-10 of fractionators C-1, C-2, and C-3, respectively. Benzene and xylene products are cooled by water in coolers E-8 and E-11 (not shown in Figure 9.1) before being sent to storage. Exchanger E-3 preheats feed to fractionator C-1 with bottoms from the same fractionator. Cooling water is supplied mainly by recycle from cooling tower T-1 by pump P-7. Electricity for all pumps and compressors, and steam for reboilers is produced from coal-fired power plant B-1. The overall input to and output from the process is represented schematically in Figure 9S.2. Figure 9S.2 Overall process streams for toluene disproportionation. Ideally, each operation in a process would be conducted in a reversible manner to achieve the minimum energy input or the maximum energy output, corresponding to a second-law thermodynamic efficiency of 100%. Even if this were technically feasible, such a process would be uneconomical because of excessive capital investment in equipment, which would have to be essentially infinite in size to minimize transport gradients. Nevertheless, it is economical to modify existing processes to reduce energy consumption, and to design new processes to operate at higher 9S-4 thermodynamic efficiencies. A second-law thermodynamic analysis identifies inefficient processes and the operations within these processes that are the most wasteful of energy, so that the process engineer can direct his or her efforts to conserving energy. 9S.2 THE SYSTEM AND THE SURROUNDINGS To conduct a second-law analysis, a process is divided into a system and surroundings. The system is the matter contained in the operating unit(s) on which the engineer wishes to focus. Everything not in the system is in the surroundings. The boundaries of the system may be real or imaginary, rigid or movable, and open or closed to the transfer of matter between the system and the surroundings. Some references call a closed system simply a system, and an open system, into and/or out of which matter can flow, a control volume. They refer to the boundary of the control volume as the control surface across which matter can flow. Batch, cyclic, and continuous processes are shown schematically in Figure 9S.3. Batch and cyclic processes are usually divided into a closed system (or simply a system) and surroundings; continuous processes are divided into an open system (or control volume) and surroundings. Figure 9S.3 Common methods of processing. 9S-5 Figure 9S.4 Partitioning of the toluene disproportionation plant. The division of a process into system and surroundings is the choice of the one performing the thermodynamic analysis. Many choices are possible for a chemical process. For example, in Figure 9S.1, the system can be the complete process, with the surroundings being the ambient air, water, and so forth, surrounding the equipment (commonly referred to as the infinite surroundings, dead state, or infinite heat reservoir) and the storage tanks for the raw materials and products. More commonly, utility plants (e.g., the steam power plant and cooling-water system) are considered separately from the rest of the process. This is shown schematically in Figure 9S.4, where the process is divided into three systems. The benzene-mixed xylenes plant is sufficiently complex that it is advisable to divide it into a reaction section and a separation section, as shown in Figure 9S.5. Any individual operation in the process - for example, fractionator C-2 - can be the system and everything else the surroundings. Finally, a portion of a single operation can be the system - for example, one tray in fractionator C-2. 9S-6 Figure 9S.5 Partitioning of the toluene disproportionation process. 9S.3 ENERGY TRANSFER Heat or work, or both, can be transferred across the boundaries of closed or open systems. If no heat is transferred across its boundaries, the system is said to be adiabatic or thermally isolated; and if neither work nor heat is transferred, the system is said to be totally isolated. The most useful kind of energy transfer is work. For example, a rotating or reciprocating shaft at the boundary of a system causes shaft work. Less useful, but more common, is heat transfer, which occurs when the temperatures of the system and the surroundings differ. If the system is at the higher temperature, it loses energy and the surroundings gain energy; and if the system is at the lower temperature, it gains energy and the surroundings lose energy. A number of devices are used in processes to transfer work between a system and its surroundings. Pumps, compressors, blowers, and fans convert shaft work into fluid energy for the main purpose of increasing fluid pressure. Turbines and expanders take energy from a fluid, causing fluid pressure to decrease, and convert the energy to shaft work for use elsewhere. A motor converts electrical work to shaft work. A generator converts shaft work to electrical work. As an example of energy transfer by work, consider Figure 9S.6(a), where an incompressible liquid at 25oC having a specific volume, V, of 0.001 m3/kg is pumped continuously at a rate m of 9S-7 10 kg/s from a pressure P1 of 0.1 MPa to a pressure P2 of 2.0 MPa, with no change in kinetic or potential energy, by a rotating shaft driven by an electrical motor.
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