Heat exchangers irreversibility

A flow diagram for the system is shown in Figure 5. Feed gas is dried, and ammonia and sulfur compounds are removed to prevent the irreversible buildup of insoluble salts in the system. Water and soHds formed by trace ammonia and sulfur compounds are removed in the solvent maintenance section (96). The pretreated carbon monoxide feed gas enters the absorber where it is selectively absorbed by a countercurrent flow of solvent to form a carbon monoxide complex with the active copper salt. The carbon monoxide-rich solution flows from the bottom of the absorber to a flash vessel where physically absorbed gas species such as hydrogen, nitrogen, and methane are removed. The solution is then sent to the stripper where the carbon monoxide is released from the complex by heating and pressure reduction to about 0.15 MPa (1.5 atm). The solvent is stripped of residual carbon monoxide, heat-exchanged with the stripper feed, and pumped to the top of the absorber to complete the cycle. 

We adopt the nomenclature introduced by Hawthorne and Davis [1], in which compressor, heater, turbine and heat exchanger are denoted by C, H, T and X, respectively, and subscripts R and I indicate internally reversible and irreversible processes. For the open cycle, the heater is replaced by a burner, B. Thus, for example, [CBTX]i indicates an open irreversible regenerative cycle. Later in this book, we shall in addition, use subscripts... 

In addition to the irreversibilities associated with these components, pressure losses (Ap) may occur in various parts of the plant (e.g. in the entry and exit ducting, the combustion chamber, and the heat exchanger). These are usually expressed in terms of non-dimensional pressure loss coefficients, Ap/(p) N, where (/ )in is the pressure at entry to the duct. (Mach numbers are assumed to be low, with static and stagnation pressures and their loss coefficients approximately the same.)... 

The nomenclature introduced by Hawthorne and Davis [4] is adopted and gas turbine cycles are referred to as follows CHT, CBT, CHTX, CBTX, where C denotes compressor H, air heater B, burner (combustion) T, turbine X, heat exchanger. R and I indicate reversible and irreversible. The subscripts U and C refer to uncooled and cooled turbines in a cycle, and subscripts 1,2, M indicate the number of cooling steps (one, two or multi-step cooling). Thus, for example, [CHT] C2 indicates an irreversible cooled simple cycle with two steps of turbine cooling. The subscript T is also used to indicate that the cooling air has been throttled from the compressor delivery pres.sure. 

The heat resulting from these irreversibilities must then be removed in order to maintain the fuel cells at a desired operating temperature. Irreversibilities and the resulting quantity of heat produced can be reduced, in general, by increasing the active area of the fuel cells, heat exchangers, and fuel reformer but increased equipment costs result. 

With single irreversible second-order reactions, the maximum of the heat release rate is reached at the beginning of the feed. At this stage, the heat exchange area may only be partially used, due to the increasing volume. This limits the effective available cooling capacity. Therefore, the knowledge of the maximum heat release... 

At this point the need arises to become more explicit about the nature of entropy generation. In the case of the heat exchanger, entropy generation appears to be equal to the product of the heat flow and a factor that can be identified as the thermodynamic driving force, A(l/T). In the next chapter we turn to a branch of thermodynamics, better known as irreversible thermodynamics or nonequilibrium thermodynamics, to convey a much more universal message on entropy generation, flows, and driving forces. 

In Section 3.3, we have shown that the entropy generation rate in the case of heat transfer in a heat exchanger is simply the product of the thermodynamic driving force X = A(l/T), the natural cause, and its effect, the resultant flow / = Q, a velocity or rate. Selected monographs on irreversible thermodynamics, see, for example, [1], show how entropy generation also has roots in other driving forces such as chemical potential differences or affinities. 

The endoreversible heat engine irreversibilities are assumed to take place only in the engine s exchange of heat with the environment. (Taken from De Vos, A., Energy Corners. Manage., 36, 1, 1995.)... 

Due to the irreversible heat exchange between the four heat reservoirs (for T0 = 300 K and T, = 600 K), the real maximum power is found to be close to a value of 0.3 rather than the ideal value of 0.5. The maximum power is found at an optimal flow rate (32 corresponding to an optimal set of temperatures T2 and T3/ satisfying the Carnot relation... 

The reaction considered is the gas-phase, irreversible, exothermic reaction A + B — C occurring in a packed tubular reactor. The reactor and the heat exchanger are both distributed systems, which are rigorously modeled by partial differential equations. Lumped-model approximations are used in this study, which capture the important dynamics with a minimum of programming complexity. There are no sharp temperature or composition gradients in the reactor because of the low per-pass conversion and high recycle flowrate. 

The point of this analysis was to characterize the source of inefficiencies in the process as designed. The main heat exchanger was the key item. The authors developed equations which related the area of the heat exchanger and its irreversible entropy change to two controllable design variables namely, the pressure drop, and the hot end temperature driving force between... 

Bejan, A., "The Concept of Irreversibility in Heat Exchanger Design Counter-flow Heat Exchangers for Gas-to-Gas Applications," Trans. ASME J. Heat Transfer, 99, 374 (1977). 

Figure 24. Autothermal reaction control with direct (regenerative) heat exchange for an irreversible reaction [14], A) Basic arrangement B) Local concentration and temperature profiles prior to flow reversal in steady state C) Variation of outlet temperature with time in steady state.

Z3 A rigid vessel 10(ft)3 in volume contains saturated-vapor steam at 75(psia). Heat exchange with a single external heat reservoir at 60(°F) reduces the temperature of the contents of the vessel to 60(°F). Determine. What is the irreversible feature of this process ... 

Here, exm is the flow-exergy destruction, or irreversibility, and T0 the reference temperature. The system will be thermodynamically advantageous only if the Nx is less than unity. The exergy destruction number is widely used in second-law-based thermoeconomic analysis of thermal processes such as heat exchangers. 

In the case of a practical heat engine an energy balance and a flow balance are made up based on knowledge of turbine blade, heat exchanger and other characteristics. An exergy account, or entropy balance, then establishes the detail of the losses or irreversibilities. No such losses occur in the equilibrium of Figure A.I. See Figure 2.2 of Barclay (1998). 

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