BINARY RANKINE CYCLE OPTIMIZATION Golub, M., Koscak-Kolin, S., Kurevija, T.

Transcription

1 BINARY RANKINE CYCLE OPTIMIZATION Golub, M., Kosak-Kolin, S., Kurevija, T. Faulty of Mining, Geology and Petroleum Engineering Department of Petroleum Engineering Pierottijeva 6, Zagreb 0 000, Croatia Tel: , Fax: mgolub@rgn.hr ABSTRACT Geopressured geothermal fluids at Croatian reservoirs ontain energy in three different forms suh as: dissolved gases and minerals, high pressure and relatively high temperatures. Natural gas must be separated for the optimal utilization effiieny, whih simultaneously maximizes the onversion proess due to the wellhead temperature. Binary Rankine yle uses a seondary working liquid, beause the temperatures of the most geothermal fluids are usually too low to be used diretly. However, behavior of representative seondary fluids is strongly dependent on harateristis of the geothermal fluid. Superheating degree in seondary yle ould be orrelated to the moleular properties of eah working fluid whih is determined by the geothermal wellhead temperatures.. INTRODUCTION Optimization of the geothermal energy prodution proess inludes minimization of all energy losses from the reservoir onditions to the end user. As the huge amount of the available field energy is mostly spent in the borehole and in the surfae equipment, proess optimization requires sientifially-researh aess, based upon the physialhemial onditions of flow and on onstrution of prodution equipment. Minimization of energy losses, whih is area of speifi sientifi interest, an be approximately divided in four interative ategories: a) Colletor parameters of the geothermal reservoirs and results of measurement data in reservoir analysis. b) Tehnial-tehnologial possibilities in aordane to the dynamial pressure gradients and to the gradients of dynamial temperatures in the well. ) Eletion of the surfae equipment of the primary yle for the geothermal water prodution and injetion. d) Choie of the thermodynami proess priniple in the seondary yle in onnetion to the field of appliation. The maximum available energy produed with the minimum irreversibility ours when the heat apaities of geothermal fluid versus seondary working fluid are onstant. These irumstanes give balaned exhanger in whih the temperature differene between this opposite streams must be kept uniform [5]. Beause of that, heat exhanger is the most important element of binary yle whih will be investigated with the speial attention.

2 . TEMPERATURE DIFFERENCE OPTIMIZATION The starting point in heat extration optimization is formula for temperature differene in irreversible proesses, whih an be found in Bošnjaković [3], page 0. This was the inspiration for a researh upon heat effiieny in geothermal systems, beause all the proesses whih are involved in energy prodution are irreversible: RT = p T T () p p This formula an be transformed in more onvenient shape through a few steps: p = = ΔT T g T w T () p/r p K p = T p p - v p R T g w = = R κ = T κ κ - p v p = f = f R p κ κ - = κ p R κ v = p - v κ v = p v κ ΔT = Tg T = K w κ (5) Main parameters used in this dedution are: ΔT = temperature differene (K) T gw = wellhead temperature of geothermal fluid (K) T = ritial temperature of working fluid (K) K = onstant in mathematial dedution p = speifi heat at onstant pressure (kj/kg K) v = speifi heat at onstant pressure (kj/kg K) R = gas onstant (kj/kg K) κ = adiabati oeffiient =, Although all real proesses are polytrophi, for the purpose of the first dedution, here it is taken an adiabati oeffiient (κ) for ideal proesses amounting,. Temperature differene (ΔT) is the parameter, analyzed as the most influening fator in heat exhange effiieny, as well as it is important thermodynami value in optimization of the whole geothermal heat and power prodution system. Seletion of seondary, working fluid with adequate ritial temperature (T ) and speifiation of the operating onditions are signifiantly dependent on: thermodynami properties of geothermal fluid, heat exhange optimization. Constant (K) in dedution has a physial meaning onneted to molar enthalpy of ideal gases, whih seems to be the same number for all ompounds above ritial onditions. v v = κ κ - (3) ()

3 3. GEOTHERMAL ELECTRICITY GENERATION On the figure it an be seen that the geothermal fluid is firstly passing through the separator (primary yle), in order to avoid damage of fin tubes in the heat exhanger. After that, heat is transformed into mehanial work as in lassial power plants, whih are working upon Clausius-Rankine proess (seondary yle) [6]. Seondary fluid from the heat exhanger is entering the turbine () and produes the power on the shaft. Next unit plant is ondensator (-3), where working fluid is ooled and pumped bak in the heat exhanger (). The heat transmission from the geothermal fluid to the seondary fluid starts again and the whole proess an be repeated. PRIMARY CYCLE SECONDARY CYCLE separator heat exhanger turbine generator 3 prodution well injetion well feed pump ondensator Figure : Sheme of geothermal power prodution The main parameter in heat usage optimization is temperature differene between geothermal fluid temperature and temperature of seondary fluid (ΔT ). An eletion of seondary fluid with the adequate ritial temperature is one of the most important step in projet evaluation, beause it must be high enough to obtain superheated steam on the turbine entrane []. As these proesses are onduted in the heat exhanger, it is analyzed separately, and this is the most important issue. 3. HEAT EXCHANGER OPTIMISATION geothermal fluid ΔT injetion well ΔT working fluid Figure : Heat exhanger of geothermal power plant There are two temperature differenes at heat exhanger, due to the irreversibility analysis of thermodynami performane : ΔT = temperature differene between geothermal water and seondary working fluid (it is taken as a onstant although during the proess it is osillating) ΔT = temperature differene between inlet and outlet of geothermal water from the heat exhanger 3

4 When two temperature differenes at heat exhanger are plotted together on same heatentropy diagram (figure 3), mutual influenes of the important elements an be easily reognized. Binary-Rankine yle on diagram is presented with typial points from to, whih are also marked on the sheme in figure. Superheated working fluid in turbine expands adiabatially from to, after whih it passes through the ondensator till the point 3. When the irulating pump returns fluid in heat exhanger, pressure is raised up, but pressure lines 3 and are so near in diagram that they an be presented as one []. T (K) T gw INLET wellhead temperature ΔT ΔTA = AVAILABLE T s T out T T e T,3 OUTLET 3 ΔT ' '' superritial temperature ritial point evaporation temperature turbine expansion ondensator temperature ΔT 3 = BALNEOLOGY T o ambient temperature s (kj/kg K) Figure 3: Heat hart of the Binary-Rankine yle Wellhead temperature of geothermal fluid is taken as inlet temperature at heat exhanger (T gw ). The temperature differene (ΔT ) depends upon temperature (T ) in ritial point of working fluid as follows: p κ ΔT = Tg T = f = f w R κ - It means that ritial temperature (T ) unambiguously defines neessary temperature of geothermal fluid, while proper temperature differene (ΔT ) is the main parameter in seletion of adequate working fluid. After the first heat transmission is obtained, temperature of geothermal fluid (T out ) at the outlet of heat exhanger is still high enough to be applied for diret energy usage. In the heat diagram (fig. 3) it is represented with available temperature differene (ΔT A ). Remaining temperature differene (ΔT 3 ) an be used for out-balane energy prodution, suh as balneology, where the temperature of used hot water is equal to ambient (T o ).

5 . HEAT EXCHANGER IRREVERSIBILITY Effiieny of heat exhanger of geothermal prodution system an be improved under following irumstanes: if there is enough heat for evaporation and superheating of seondary fluid; if the ontat of geothermal fluid and seondary fluid is as long as it is neessary to reah final temperature differene between primary and seondary yle (ΔT ), as shown on piture. PRIMARY SECONDARY PRIMARY PRIMARY high ΔT low ΔT high low Figure : Heat exhanger effiieny In ontrast to the finite system whih eventually omes to equilibrium with its environment, no definite end state an be assigned to a proess in whih energy is withdrawn from a hot reservoir, suh as a geothermal. These deposits, by definition, never ome to equilibrium with the environment and it is meaningless to speak of the maximum amount of useful work, but not to mention frition effets and the onept of thermodynami irreversibility [5]. For any proess in ation with the hange of thermodynami state, the irreversibility funtion is a measure of work whih is lost aording to frition of finite temperature differenes inurred aross the heat exhanger. In the ase of superheat binary yle with the main element heat exhanger, the irreversibility would be: the produt of an ambient temperature T o and heat produed by the geothermal fluid affeted to seondary working fluid, divided by finite temperature differene (ΔT ): To (i - i ) I = ΔT Tg high Tglow ΔT T T gw wf dt g w T o = ambient temperature (K) i, i = speifi enthalpy in heat hart (fig. 3) (kj/kg) ΔT = temperature differene of geothermal water at the heat exhanger (K) T gw = T g high = wellhead temperature of geo-fluid (K) T g low = outlet temperature of geothermal fluid (K) ΔT = temperature differene between geothermal water and seondary working fluid (K) T wf = temperature of seondary working fluid (K) (6) 5

6 Irreversibility in the other word is defined as the differene between the maximum useful work that an be obtained and the atual useful work. In the reversible proess those two works divided would be zero. In opposite, the effetiveness of proess or effiieny is the ratio of the atual to the maximum useful work, what shall be presented in the next artile, applied to heat exhanger optimization. 5. CONCLUSION Heat exhanger will be at the interfae between the geothermal fluid and the working fluid and will onstitute the most essential omponent of the Binary Rankine yle power plant. A general approah is given here to show the effet of system parameters. The basi orrelation is thermodynami developed and is stressed upon to the oeffiient K whih has a physial meaning, what to be pointed out and will be investigated in the next artile, regarding to our experimental geothermal data, for single fluid yle optimization. This will be done between the high and low temperature side (ΔT ) of a vertial ounter flow, shell and tube heat exhanger designed for the utilization of hydrothermal systems in Croatia at moderate temperatures, for an adequate working fluid hoie. REFERENCES. Austin, A. L., (975), Prospets for advanes in energy onversion tehnologies for geothermal energy development, Proeedings of the Seond UN Symposium on the development and use of geothermal resoures, San Franiso, Vol. 3, p Bird, R. B., Stewart W. E. & Lightfoot, E. N., (960), Transport phenomena, John Wiley and Sons, In., pp Bošnjaković, F. (96), Nauka o toplini (Siene upon heat), Tehnička knjiga, Zagreb, pp 35. Kolin, I. (967) Thermodynamis Atlas, Longmans, London, pp MAdams, W. H. (95), Heat transmission, MGraw-Hill book Co. third edition, pp Milora, S. L., Tester, J. W., (976), Geothermal energy as a soure of eletri power, The MIT Press, pp 86 6