Lost work entropy production

When a process is completely reversible, the equahty holds, and the lost work is zero. For irreversible processes the inequality holds, and the lost work, that is, the energy that becomes unavailable for work, is positive. The engineering significance of this result is clear The greater the irreversibility of a process, the greater the rate of entropy production and the greater the amount of energy that becomes unavailable for work. Thus, every irreversibility carries with it a price. 

In Chapter 2, we pay a renewed visit to thermodynamics. We review its essentials and the common structure of its applications. In Chapter 3, we focus on so-called energy consumption and identify the concepts of work available and work lost. The last concept can be related to entropy production, which is the subject of Chapter 4. This chapter shows how some of the findings of nonequilibrium thermodynamics are invaluable for process analysis. Chapter 5 is devoted to finite-time finite-size thermodynamics, the application of which allows us to establish optimal conditions for operating a process with minimum losses in available work. 

In this chapter, we show that it is not so much energy that is consumed but its quality, that is, the extent to which it is available for work. The quality of heat is the well-known thermal efficiency, the Carnot factor. If quality is lost, work has been consumed and lost. Lost work can be expressed in the products of flow rates and driving forces of a process. Its relation to entropy generation is established, which will allow us later to arrive at a universal relation between lost work and the driving forces in a process. 

With X, approaching zero, lost work will approach zero, but this result is not very realistic as flows will tend to become zero too. In practice, we deal with an equipment of finite size that we wish to operate in finite time. So, the question arises With these constraints, what is the minimum amount of lost work Thus, it is clear that minimization of lost work and thus of entropy production is a challenging subject with many aspects. 

The expansion of the natural gas is a spontaneous process and thus work must have been lost. According to the Gouy-Stodola relation, this lost work is related to the entropy production of the process. 

As an example, let us consider a feedwater heater, such as illustrated by Component No. 6 in Figure No. 1. Let Z represent the annualized capital cost (say in dollars per year) of owning and operating the feedwater heater (including maintenance, overhead, etc., as well as interest). Also, let X represent the unit cost of each type of lost work, while T0 represents the lost work, where represents the rate of entropy creation (or production) corresponding to each type of lost work in the feedwater heater (2, 6,7). Then let A, Ag, and Ah represeht the unit costs of lost work Td a T0 b, and T h due respectively to head loss (pressure drop) in the feedwater A, head loss in the condensing steam B, and heat transfer (temperature drop) from the condensing steam.to the feedwater, denoted by H, so that the total annualized cost T attributable to the feedwater heater is,... 

Determine and compare the rate of entropy production and the lost work for these two mixing processes producing a product of stream 3. 

These two simple examples show that mixing the saturated steam with the superheated steam in the second mixing process causes much greater entropy production and lost work potential than mixing two saturated steams in mixing process 1. 

Example 4.8 Chemical reactions and reacting flows The extension of the theory of linear nonequilibrium thermodynamics to nonlinear systems can describe systems far from equilibrium, such as open chemical reactions. Some chemical reactions may include multiple stationary states, periodic and nonperiodic oscillations, chemical waves, and spatial patterns. The determination of entropy of stationary states in a continuously stirred tank reactor may provide insight into the thermodynamics of open nonlinear systems and the optimum operating conditions of multiphase combustion. These conditions may be achieved by minimizing entropy production and the lost available work, which may lead to the maximum net energy output per unit mass of the flow at the reactor exit. 

Example 4.25 Column Exergy efficiency Propylene-propane mixture is a close boiling mixture. A reflux ratio of 15.9 (close to minimum) and 200 equilibrium stages are necessary. Table 4.13 shows the enthalpy and entropies of the saturated feed and saturated products from the simulation results with the Redlich-Soave equation of state. The reboiler and condenser duties are 8274.72 and 8280.82 kW, respectively. The reference temperature is 294 K. The lost work ZTFis obtained from Eq. (4.198) as... 

The first term on the left of this equation is the thermodynamic force. The force is not necessarily constant when we have minimum lost work. The optimum force that gives the minimum total entropy production rate is obtained from... 

To reduce the lost work in industrial process plants, the minimization of entropy production rates in process equipment is suggested as a strategy for future process design and optimization [81]. The method is based on the hypothesis that the state of operation that has a minimum total entropy production is characterized by equipartition of the local entropy production. In this context we need to quantify the entropy sources of the various irreversible unit operations that occur in the industrial system. 

In a steady state and adiabatic mixing process 4.5 kg/s of superheated steam at 798.15 K and 6000 kPa is mixed with a saturated steam at 2319.8 kPa. If the output stream is at 565 K estimate the rate of entropy production and lost work. 

The product of thermodynamic forces and fiows yields the rate of entropy production in an irreversible process. The Gouy-Stodola theorem states that the lost available energy (work) is directly proportional to the entropy production in a nonequilibrium phenomenon. Transport phenomena and chemical reactions are nonequilibrium phenomena and are irreversible processes. Thermodynamics, fiuid mechanics, heat and mass transfer, kinetics, material properties, constraints, and geometry are required to establish the relationships... 

Generally, a chemical reaction has a nonlinear relation between the rate and the driving force AIT. Chemical reactors are often designed to operate at the maximum rate of reaction. An alternative is a reactor operated with minimum useful work lost. The lost work per unit time in a chemical reactor is given by the Gouy—Stodola theorem, and is obtained by integrating the entropy production rate over the reactor volume ... 

Finally, Example 8 is more complex in that it comprises entropy production due to chemical reaction in combination with heat transfer, and also diffusion the role of the latter appears as marginal. The example can also be regarded as an example of complex single-node balancing, a kind of thermodynamic analysis included. Concerning the entropy production (or loss of exergy), it turns out that the chemical portion, thus the term -(Gr / Tj ) Wr in (6.2.109) can represent an enormous item in the exergy balance it can be computed, but this is usually all that we can do in practice. In other terms, what kind of work has been actually lost, is a matter of theoretical speculations only. 

The lost work is the dilference between these expressions, leading to the definition of the second law efficiency Wideai/ V- Maximum efficiency means minimum entropy production. 

The hypothesis was also used to predict the optimal state of a hypothetical packed distillation column. The optimal path of operation as determined from eqs 14.70 and 14.71, confirmed the hypothesis, giving constant entropy production in the rectifying and stripping sections of the column. Doing distillation along these lines, one can save up to 50 % of the lost work. " Constructional changes will, however, be needed in the column. 

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