I am not so sure. It depends also on how you calculate costs, and where your boundaries for 'overall' are. The more inclusive you try to make your calculation, the less well defined your boundary conditions will be. Also, a corollary of a 'yes' answer must be that the cheaper a system, the more efficient it will be - which is clearly not necessarily true and in many cases is demonstrably false, else why do agencies try so hard to increase efficiency and make things more expensive in the process. I think you need to define particular cases and evaluate each one to determine your answer.

I think you should implement a separate analysis for each one.

But cost is important to us, isn't it?

Why should we minimize exergy?

Minimum cost is important than exergy, isn't it?

If overall cost is minimum but exergy is maximum, what is it mean? Is it possible?

Dear Steffen,

"Exergy (in older usage, available work and/or availability) of a system is the maximum useful work possible during a process that brings the system into equilibrium with a heat reservoir." (From Wiki). Thus exergy destruction is an ugly cousin that we don't want to face. But in most cases exergy efficiency and the exergy destruction are related with your definition (Yes, unfortunately there is not an exact definition and above definition is the most common one)

Thus, if in your definition, the exergy destruction parameters are related with your cost parameters. Than yes, most probably your exergy destruction reduction will be parallel to costs. But note that, fixed costs such as labor costs etc. may have no influence on the thermodynamic parameters (such as on the exergy destruction). Moreover, (related with your definitions) some thermodynamic parameters can also be irrelevant with the exergy destruction.

Now, the answer of your question is; it does not have to be always, it is not a must.

hi

i think it is true because exergy destruction lead our cycle to consume more energy and this increment makes high cost!

regards

@ George Tsatsaronis

There is a week correlation between exergy lost and economical characters. The reason is, that many of the factors effect only the first group of those and many factors only the second group. Example: if the share of PV power plants is high the average price of the electric energy will be high (one must invest a lot of money for "classic" power plants which will be loaded in early mornings, evenings and nights only -- this investition cost is reflected in the energy price*). In this situation the high exergy efficiency of the new power plants has secondary importance. The answers arrived till now assume homogeneous electric energy systems, with the same main characteristics as the ones of the investigated facility.

________________________

* Additional source of the problems is the preference of PV plants, including the financial support by the goverments.

Both are seperate objectives. Decreased destruction leads to higher plant performance and hence higher amount of product. Lower product cost is significantly function of plant life and fuel costs even though lower exergy destruction would also favor final costs. Therefore there are multiobjective optimization tools for optimal conditions. I believe the answer is no for most cases.

Example: Single flash geothermal power plants are low efficient. However there are not many components required for power conversion and cost of electricity might be as low as 1.8 cents/ kWh. If binary geothermal plant would be utilized, much higher efficincies could be obtained for the same conditions where product costs would result in 2.5- 3 cents/kWh.

You may try simple GA tools in Matlab for multi-objective optimization for conditions that lead to higher plant performance and lowet product costs.

Yes, because when u are minimizing cist of a system then you are reducing its output,so u are also reducing exergy.Exergy is energy that is available for use

Yes, the minimization of exergy losses will increase the optimal performance of the plant, or the operating cost is involved to overcome these losses. So by performing exergy analysis the identification of exergy losses and overcoming during design stage or some modification will enhance the better optimization of available resources.

Not necessarily...

Refer to the exergoeconomic analysis theory we have two cost source in most thermodynamic systems: 1) The costs that come from exergy destructions and losses because of low exergetic efficiency. or in other case we say the operation and maintenance costs. 2) The costs that are because of high equipment purchase prices. in other case we say the capital costs. by minimizing the exergy destruction you can only decrease operation and maintenance costs of system; while for purchasing high efficiency equipment you should pay high capital cost... so we can not always conclude that minimizing overall cost cause to less exergy destruction.

I can't clearly understand why exergy (useful energy or maximum obtainable work) is used for thermo-economics..?

It is obvious that exergy considers all destruction and interaction of the system with surrounding....but i think it's not good reasons...

so what is the physical meaning of exergeo-economics?

for example what is the physical meaning of C=10($/h) as we know it's calculated by exergy?

>>>>>> Is this cost true and sensible?

@Steffen Schmid

If one calculates the enthalpy-based efficiency of a power plant, the result is about 30..40 %, because the enthalpy loss in the condenser is large. The possibility to decrease of this loss is limited by the T0 temperature of the cooling water. It can be seen in the definition of the e specific exergy:

e = h - T0s, (h: enthalpy, s: entropy)

therefore the enthalpy-based efficiency is out of our control.

In the boiler, the enthalpy is higher than in the condenser. If the entropy is small, the specific exergy of the fresh steam is much higher than in the condenser. The increasing entropy decreases the maximum obtainable work.

Theoretically the entropy-analysis is equivalent with the exergy-analysis. Nevertheless, for practical reasons, the exergy-analysis is the common procedure.(Example: the heat transfer in the boiler is the source for increasing entropy, due to the high temperature difference. The loss in the maximum obtainable work is mainly originated from the boiler. It means that the boiler is the weak point of the power plant.) The unit of the specific exergy is kJ/kg, well usable in the engineering calculations. The product of e and the mass flow (kg/s) is measured in kW, and the exergy loss in the different parts of the power plant will show the places of the necessary designer's actions. (This walue can be munltiplies by the price of the electric energy of the power plant, and the economists can understand the problem without energetic knowledge.)

sorry for my another question:

Why the cost per unit of exergy of the working fluid before and after a turbine remains constant (ci=ce)?

Exergy is change in the turbine but the cost per unit of exergy ($/GJ) remains constant?

Dear all

I can't understand how we consider auxiliary equation for cost analysis, for example what is the meaning of this kind of sentences in Bejan's book:

"Since the purpose of such a heat exchanger is to heat the cold stream and exergy is removed from the hot stream, the average cost per exergy unit for the hot stream remains constant and is equal to the average cost at which each exergy unit of stream 3 was supplied in upstream components."

why the average cost per exergy unit for the hot stream remains constant?

Egon, you state that the boiler is the weak point of the power plant. The way you have worded it seems to mean that if you left the boiler out, the power plant would work better. I would rather say that the power plant is limited by the physical properties of the working fluid. If you could operate between 1500C and 50C you would have a splendidly efficient plant. But you can't.

I think that the statement that the cost of exergy remains constant should be understood to mean that the cost of putting the energy into the working fluid hasn't changed, as that is an upstream issue. Of course you won't be able to get so much energy back out below the turbine, so in this sense the cost per exergy unit has increased. I agree that the statement is misleading; I like to think it got missed in the proofreading (if there was any).

@Tony Maine

The "weakness" means that the boiler is the place where the cost/benefit ratio is minimal. (The robustness of the whole power plant here is the weakest.) Example: the heat transfer leads to the increment of the entropy therefore to the loss of exergy. Compare the average temperature differences in a 9 MPa/535 oC boiler and a supercritical (double) reheated boiler (the working fluid is the same H2O). The cost of the smaller exergy loss is the more complicated facility, and the benefit is the better efficiency. The results of similar actions for other elements of the power plant are the higher cost/benefit ratios. If the cooling surface in the condenser would be infinite, the temperature difference would be zero. And what about the efficiency of the whole power plant? (See the problematics of the Hungarian Heller-Forgó system with mixing condenser, which is quasi infinite large. This system is very useful for countries in deserts. Introduction can be found in Wikipedia.)  

A special type of the heat sources is the nuclear reactor. The above statements remain valid for these, as well. The efficiency of the nuclear power plants with tank-type reactor (PWR, BWR) is limited (~35 %) due to the condition that the working temperature is much below the critical one (373.946 oC) since the critical pressure (22.046 MPa) would be too high for the tank. Note: the temperature inside a fuel element may be as high, as the melting temperature of UO2 (3120 K).

The 4th generation gas-cooled reactors are free from the limit by critical parameters, their working temperature may be even ~1000 oC, resulting in improved efficiency (by +20..+50 %). A survey: https://www.iaea.org/NuclearPower/Downloadable/Meetings/2015/2015-08-25-08-28-NPTDS/DAY1/2._HTGRs_-_Technology_overview_and_related_IAEA_activities.pdf

Generally, the usual optimization criteria of a system are the energy efficiency, the exergy efficiency and a financial index (for example the NPV maximization or the payback period minimization). Optimizing a system with these criteria separately, generally, lead to three different optimum scenarios which can be similar or totally different. A solution to the global optimum design is the use of a multi-objective optimization/evaluation method.

About the initial question, first, you can consider that minimum exergy destruction practically mean maximum exergy efficiency.

- The energy efficiency is an index that takes into account the heat rates.

- The exergy efficiency is an index that takes into account the heat rates and their temperature levels (maybe also other parameters - in the fuels for example - but in simple cases the temperature).

- The financial analysis takes into account the heat rates, the system scale (please take into account that the smaller installations have greater specific cost) and the cost of energy/electricity/cooling or of everything useful product.

The previous bullets make clear that the three criteria are totally different. The main difference between the exergy and the financial optimization is that exergy takes into account the operating temperature level, while the financial analysis takes into account the cost.

BUT in many cases, the costs have values which correspond to the used temperatures levels or the kind of the energy rate. In other words, the exergy analysis gives higher weight in electricity production than heating production in a system, while the price of selling the electricity is higher than selling the heating. So, in many cases, the optimization leads to the same direction and there is increased possibility to have similar maximum points by optimizing with exergy and with financial criteria.

To conclude, the optimization with exergy efficiency optimization (or exergy destruction minimization) usually leads to an optimum scenario which is close to the financial optimum choice. However, it is not in all the cases correct because you can consider that using the electricity cost between two countries with totally different market prices makes this optimization not to be in the same direction with the two criteria.

Dear

Minimisation of exery destruction will reduce operating costs only. If you are purchasing lower quality product at cheap rate...do not expect minimum exergy destruction

Reducing the overall cost of the system or cycle does not lead a reduction in exergy destruction, but in terms of exergoeconomics it will reduce the cost rate of exergy destruction ($/hr). The exergoeconomics study is use to inculcate both economics and thermodynamics principles into it. Therefore an exergoeconomic optimization would lead to a reduction in cost rate of exergy destruction.

Agree with Tony Maine ....

Please share me the best answer might you trust...

Regards…

Controlling the exergy destruction may be reduced operating cost of the system.