EXERGY ANALYSIS OF THERMAL PROCESSE

EXERGY ANALYSIS OF THERMAL PROCESSES AND SYSTEMS WITH ECOLOGICAL APPLICATIONS

J. Szargut
Institute of Thermal Technology, Technical University of Silesia, Poland Keywords: Exergy, Thermal Processes, Ecological Application, Energy. Contents
1. Definition of Exergy
2. Exergy Losses, Exergy Balance, and Exergy Efficiency
3. Calculation of Exergy
4. Applications of Exergy Analysis
5. Comparison of the Energy and Exergy Balance of Selected Processes
6. Cumulative Consumption of Exergy
7. Partial Exergy Losses in Thermal Systems
8. Ecological Application: Depletion of Natural Exergy Resources Bibliography
Biographical Sketch

Summary

The definition of exergy has been formulated. The law of Gouy-Stodola, expressing the unavoidable and unrecoverable exergy losses, has been discussed. The exergy efficiency determining the deviation from thermodynamic perfection has been defined. The equation of exergy balance has been formulated. The calculation methods of the physical and chemical exergy have been explained. As the reference species determining the reference level of chemical exergy, the gaseous components of air, the ions or molecules dissolved in seawater and the solid compounds present in the external layer of the Earth’s crust have been assumed. Practical rules of the improvement of thermal processes have been presented. The energy and exergy balances of typical processes (thermal power plant, refrigerator) have been compared. The problems of exergy analysis of thermal systems have been discussed. It is based upon the analysis of cumulative exergy consumption and of partial exergy losses appearing in all the links of the system. The cumulative consumption of non-renewable natural exergy resources has been accepted as the measure of the ecological cost. Exemplary values of the domestic ecological cost have been cited.

1. Definition of Exergy

In Figure 1 the hydraulic and thermal power plants are compared. The hydraulic power plant utilizes the difference of the levels of water in the higher and lower reservoir. Similarly the thermal power plant utilizes the temperature difference between the hot heat source and cold heat sink. However there exists a great difference between the considered power plants. The hydraulic power plant can (after elimination of friction) convert into work the total potential energy of water taken from the higher reservoir.



However, as Carnot (1824) discovered, the thermal power plant (even operating without any losses) can convert into work only some part of the heat taken from the hot source.


Figure 1. Comparison of the hydraulic and thermal power plant


The law of Carnot has the form:

W  Q T1  T2
T1




(1)


where T1, T2 denote the absolute temperature of the hot source and cold sink of heat. The heat from the hot source can be best utilized if a natural (not payable and practically non-limited) cold sink can be used. The natural environment represents such a heat sink or source. Hence the quality of heat is not constant, and depends on the absolute temperature of the heat source and the temperature of the natural environment. This quality can be expressed by means of the maximum ability to perform work between the mentioned heat reservoirs:


Wmax

 Q T  T0
T


(2)


where

T0 absolute ambient temperature,
(T-T0)/T dimensionless Carnot-factor characterizing the quality of heat taken from the source with a constant temperature.



The amount of the performed work could be greater than that resulting from Eq. (2), but it would require the use of an artificial sink of heat, created by means of other valuable kinds of energy instead of the natural environment.

Eq. (2) relates only to the ideal reversible processes. According to the second law of thermodynamics, all real processes are irreversible. In real processes the amount of performed work is always smaller than that resulting from Eq. (2). Hence Eq. (2) characterizes the maximum attainable amount of the performed work.

Also other kinds of energy differ in their ability to be transformed into other kinds of energy. For example, internal energy can be only partially transformed into mechanical energy (kinetic or potential) or into mechanical work. It is worth stressing, that the ability of some streams of matter to drive thermal processes (e.g. of the stream of compressed air) cannot be characterized in terms of energy (the energy of the compressed air at ambient temperature equates to the energy of the atmospheric air).

The ability to perform mechanical work has been accepted as a measure of the quality of various kinds of energy, characterizing their ability to be transformed into other kinds of energy. This ability depends not only on the composition and state parameters of the considered matter (determining its energy), but also on the composition and state parameters of the matter commonly appearing in the environment of the considered transformation process. The mentioned environmental parameters should determine the reference level for the calculation of the discussed quality index.

The explained quality index of energy has been termed by Z. Rant as exergy. It expresses the maximum work output attainable in the natural environment, or a minimum work input necessary to realize an opposite process. The second version proposed by Riekert is very convenient and can be formulated as follows:

Exergy is a shaft work or electrical energy necessary to produce a material in its specified state from materials common in the natural environment, in a reversible way, heat being exchanged only with the environment.

In comparison with energy (being a function of state of the considered matter only) exergy is a function of state of the considered matter and of the common components of the environment.

2. Exergy Losses, Exergy Balance, and Exergy Efficiency

All real processes are irreversible. The irreversibility involves an increase of the sum of entropy values of all the bodies taking part in the analyzed process. In order to apply this principle, an isolated system comprising all the bodies taking part in the process should be defined. Some components of this system can change their state in the direction of decreasing the entropy, others display an increase, but the sum of increases is always greater than that of decreases. The irreversibility always results in an unrecoverable loss of exergy. According to the Law of Gouy-Stodola, its value is proportional to the sum S of entropy increases of all the bodies taking part in the process:




 B  T0 S

(3)


Internal and external exergy losses can be distinguished. Internal exergy losses appear inside the analyzed process. External exergy losses occur after the rejection of waste products of the process to the environment. The composition and state parameters of the waste products equalize each other irreversibly with those of the environment, which causes the destruction of the exergy of waste products. External exergy loss can be calculated by means of Eq. (2), but it can be more simply expressed as the exergy value of the waste product.

The exergy analysis is based upon the assumption of a constant chemical composition of the environment. In reality the emission of some waste products changes this composition. Most important is the emission of CO2. Its concentration in the atmosphere increases due to the industrial and non-industrial emission, which can evoke the climatic changes. However it is actually not possible to evaluate the damages due to the increase of the CO2 concentration. Therefore the external exergy loss resulting from the content of CO2 in waste products is calculated as the maximum work which can be performed during the expansion of CO2 to the actual partial pressure in the atmosphere.

The main causes of exergy losses are:

a) friction (mechanical or hydraulic),
b) irreversible heat transfer (at a finite temperature difference or temperature gradient),
c) irreversible diffusion (at a finite concentration difference or gradient).

Exergy losses are unavoidable, but they should always be economically justified. Usually a limitation of the investment cost can be attained only thanks to some degree of irreversibility. For example, the heat transfer area of a heat exchanger has a finite value only if the temperature difference of the considered fluid streams is greater than zero in all its cross-sections. Exergy loss not having any economical justification, should be treated as the result of an error in the art of engineering.

According to Eq. (2) exergy is exempt from the law of conservation. Therefore the exergy balance should be closed by means of the internal exergy loss if the system boundary comprises only the analyzed process, without the environment. The balance equation contains: the exergy Bd of the delivered bodies; the exergy increase Bs of the system; the exergy of the bodies carried off from the system (which can be divided into the exergy Bau of useful products and the exergy Baw = Be of waste products, expressing the external exergy loss); the sum of exergy increases Bq of external heat sources operating on the system boundary; the work W performed by the system, and the internal exergy loss B:


Bd  Bs  Bau  Bq  W   B

(4)


The increase of exergy of the external source of heat results from Eq. (2):




Bq

 Q T  T0
T


(5)


where

Q heat delivered to the system from the heat source,
T temperature measured at the system boundary in the place of heat delivery.

The exergy of a heat source being warmer than the environment, decreases during the heat extraction. However the extraction of heat from a source colder than the environment increases the exergy of this source. So the operation of a refrigerator increases the exergy of the refrigerated chamber, thanks to the consumption of the valuable driving energy (driving exergy) and

Kết quả (Việt) 1:

EXERGY PHÂN TÍCH CỦA CÁC QUÁ TRÌNH NHIỆT VÀ CÁC HỆ THỐNG VỚI CÁC ỨNG DỤNG SINH THÁIJ. SzargutViện nhiệt công nghệ, kỹ thuật đại học Silesia, Ba Lan từ khóa: Exergy, quá trình nhiệt, ứng dụng sinh thái, năng lượng. Nội dung1. định nghĩa của Exergy2. Exergy thiệt hại, Exergy cân bằng và hiệu quả Exergy3. tính toán Exergy4. ứng dụng của Exergy phân tích5. so sánh của năng lượng và Exergy số dư của quá trình được chọn6. tích lũy tiêu thụ của Exergy7. một phần Exergy thiệt hại trong hệ thống nhiệt8. sinh thái ứng dụng: Sự suy giảm của tự nhiên Exergy tài nguyên thư mụcTiểu sử ký họaTóm tắtĐịnh nghĩa của exergy đã được hình thành. Pháp luật của Gouy-Stodola, thể hiện những thiệt hại không thể tránh khỏi và không thể khôi phục exergy, đã được thảo luận. Hiệu quả exergy xác định độ lệch từ thăng giáng nhiệt hoàn hảo đã được xác định. Phương trình của sự cân bằng exergy đã được hình thành. Phương pháp tính toán của vật lý và hóa học exergy đã được giải thích. Như loài tham chiếu xác định mức độ tham khảo của hóa chất exergy, các thành phần khí của máy, các ion hoặc phân tử hòa tan trong nước biển và các hợp chất rắn hiện diện trong các lớp bên ngoài của lớp vỏ trái đất đã được giả định. Các nguyên tắc thực tế của việc cải thiện quá trình nhiệt đã được trình bày. Cân bằng năng lượng và exergy của quá trình điển hình (nhà máy nhiệt điện, tủ lạnh) đã được so sánh. Các vấn đề của exergy phân tích của nhiệt hệ thống đã được thảo luận. Nó dựa trên phân tích tích lũy exergy tiêu thụ và thiệt hại một phần exergy xuất hiện trong tất cả các liên kết của hệ thống. Tích lũy tiêu thụ tài nguyên không tái tạo tự nhiên exergy đã được chấp nhận như là các biện pháp của chi phí sinh thái. Các giá trị điển hình của chi phí sinh thái trong nước đã được nêu ra.1. định nghĩa của ExergyTrong hình 1 nhà máy điện thủy lực và nhiệt được so sánh. Nhà máy điện thủy lực sử dụng sự khác biệt của các cấp độ của nước trong các hồ chứa cao hơn và thấp hơn. Tương tự như vậy, nhà máy nhiệt điện sử dụng sự khác biệt nhiệt độ giữa các nguồn nhiệt nóng và lạnh tản nhiệt. Tuy nhiên, có tồn tại một sự khác biệt lớn giữa các nhà máy điện được coi là. Thủy lực nhà máy điện có thể (sau khi loại bỏ ma sát) chuyển đổi thành công việc tất cả tiềm năng năng lượng của nước Lấy từ các hồ chứa cao. Tuy nhiên, như Carnot (1824) phát hiện, nhà máy nhiệt điện (thậm chí hoạt động mà không có bất kỳ thiệt hại) có thể chuyển đổi thành công việc chỉ là một số phần của nhiệt Lấy từ nguồn gốc nóng.Hình 1. So sánh các nhà máy thủy lực và nhiệt điện Pháp luật của Carnot có dạng:W  Q T1  T2T1 (1) nơi T1, T2 biểu thị nhiệt độ tuyệt đối của nguồn nóng và lạnh tản nhiệt. Nhiệt từ nguồn nóng có thể được sử dụng tốt nhất nếu một tự nhiên (không phải nộp và thực tế không giới hạn) lạnh bồn rửa có thể được sử dụng. Môi trường tự nhiên đại diện cho tản nhiệt hoặc nguồn. Do đó chất lượng nhiệt không phải là liên tục, và phụ thuộc vào absolute temperature nhiệt nguồn và nhiệt độ môi trường tự nhiên. Chất lượng này có thể được thể hiện bằng phương tiện của khả năng tối đa để thực hiện công việc giữa các hồ chứa được đề cập nhiệt: Wmax  Q T  T0T (2) nơiNhiệt độ môi trường xung quanh t0 tuyệt đối,(T-T0)/T dimensionless Carnot-factor characterizing the quality of heat taken from the source with a constant temperature. The amount of the performed work could be greater than that resulting from Eq. (2), but it would require the use of an artificial sink of heat, created by means of other valuable kinds of energy instead of the natural environment.Eq. (2) relates only to the ideal reversible processes. According to the second law of thermodynamics, all real processes are irreversible. In real processes the amount of performed work is always smaller than that resulting from Eq. (2). Hence Eq. (2) characterizes the maximum attainable amount of the performed work.Also other kinds of energy differ in their ability to be transformed into other kinds of energy. For example, internal energy can be only partially transformed into mechanical energy (kinetic or potential) or into mechanical work. It is worth stressing, that the ability of some streams of matter to drive thermal processes (e.g. of the stream of compressed air) cannot be characterized in terms of energy (the energy of the compressed air at ambient temperature equates to the energy of the atmospheric air).The ability to perform mechanical work has been accepted as a measure of the quality of various kinds of energy, characterizing their ability to be transformed into other kinds of energy. This ability depends not only on the composition and state parameters of the considered matter (determining its energy), but also on the composition and state parameters of the matter commonly appearing in the environment of the considered transformation process. The mentioned environmental parameters should determine the reference level for the calculation of the discussed quality index.The explained quality index of energy has been termed by Z. Rant as exergy. It expresses the maximum work output attainable in the natural environment, or a minimum work input necessary to realize an opposite process. The second version proposed by Riekert is very convenient and can be formulated as follows:Exergy is a shaft work or electrical energy necessary to produce a material in its specified state from materials common in the natural environment, in a reversible way, heat being exchanged only with the environment.In comparison with energy (being a function of state of the considered matter only) exergy is a function of state of the considered matter and of the common components of the environment.2. Exergy Losses, Exergy Balance, and Exergy EfficiencyAll real processes are irreversible. The irreversibility involves an increase of the sum of entropy values of all the bodies taking part in the analyzed process. In order to apply this principle, an isolated system comprising all the bodies taking part in the process should be defined. Some components of this system can change their state in the direction of decreasing the entropy, others display an increase, but the sum of increases is always greater than that of decreases. The irreversibility always results in an unrecoverable loss of exergy. According to the Law of Gouy-Stodola, its value is proportional to the sum S of entropy increases of all the bodies taking part in the process:  B  T0 S (3) Internal and external exergy losses can be distinguished. Internal exergy losses appear inside the analyzed process. External exergy losses occur after the rejection of waste products of the process to the environment. The composition and state parameters of the waste products equalize each other irreversibly with those of the environment, which causes the destruction of the exergy of waste products. External exergy loss can be calculated by means of Eq. (2), but it can be more simply expressed as the exergy value of the waste product.The exergy analysis is based upon the assumption of a constant chemical composition of the environment. In reality the emission of some waste products changes this composition. Most important is the emission of CO2. Its concentration in the atmosphere increases due to the industrial and non-industrial emission, which can evoke the climatic changes. However it is actually not possible to evaluate the damages due to the increase of the CO2 concentration. Therefore the external exergy loss resulting from the content of CO2 in waste products is calculated as the maximum work which can be performed during the expansion of CO2 to the actual partial pressure in the atmosphere.
The main causes of exergy losses are:

a) friction (mechanical or hydraulic),
b) irreversible heat transfer (at a finite temperature difference or temperature gradient),
c) irreversible diffusion (at a finite concentration difference or gradient).

Exergy losses are unavoidable, but they should always be economically justified. Usually a limitation of the investment cost can be attained only thanks to some degree of irreversibility. For example, the heat transfer area of a heat exchanger has a finite value only if the temperature difference of the considered fluid streams is greater than zero in all its cross-sections. Exergy loss not having any economical justification, should be treated as the result of an error in the art of engineering.

According to Eq. (2) exergy is exempt from the law of conservation. Therefore the exergy balance should be closed by means of the internal exergy loss if the system boundary comprises only the analyzed process, without the environment. The balance equation contains: the exergy Bd of the delivered bodies; the exergy increase Bs of the system; the exergy of the bodies carried off from the system (which can be divided into the exergy Bau of useful products and the exergy Baw = Be of waste products, expressing the external exergy loss); the sum of exergy increases Bq of external heat sources operating on the system boundary; the work W performed by the system, and the internal exergy loss B:


Bd  Bs  Bau  Bq  W   B

(4)


The increase of exergy of the external source of heat results from Eq. (2):




Bq

 Q T  T0
T


(5)


where

Q heat delivered to the system from the heat source,
T temperature measured at the system boundary in the place of heat delivery.

The exergy of a heat source being warmer than the environment, decreases during the heat extraction. However the extraction of heat from a source colder than the environment increases the exergy of this source. So the operation of a refrigerator increases the exergy of the refrigerated chamber, thanks to the consumption of the valuable driving energy (driving exergy) and