$($turkish$)$

In order to convert the geothermal energy in a hot water reservoir into qualified and useful electrical energy, the process shown schematically below is applied. The hot water reservoir $(1)$ contains saturated liquid water at a temperature of $523$ K$.$Reservoir The pressure at the exit point of the well $(2)$ is $700$ kPa and the hot water is isentropically transported from the bottom of the reservoir $(1)$ to the exit point of the well $(2)$ where it exits to the surface. The vapour$/$liquid mixture entering the flash separation unit $(3)$ is isenthalpically expanded to a pressure of $270$ kPa and the vapour fraction $(5)$ resulting from this expansion drives a turbine unit. The flow $(6)$ leaving the turbine unit with a pressure of $15\mathrm{.}76$ kPa enters a condensing unit and leaves this unit as saturated liquid water with a pressure of $15\mathrm{.}76$ kPa $(7).$ Determine the conversion efficiency for this process, i$.$e$.$ the ratio of the amount of power produced in the turbine to the total amount of available power in the fluid at the outlet of the geothermal well $(2).$ Assume that the turbine unit operates isentropically$.$

$($turkish$)$

Bir s$$cak su rezervuar$$ndaki jeotermal enerjiyi, nitelikli ve kullan$$l$$ elektrik enerjisine d$$n$$t$$rmek amac$$yla$,$ a$$a$$da $$ematik olarak g$$sterilen proses uygulanmaktad$$r$.$S$$cak su rezervuar$(1),523$ K s$$cakl$$ndaki doygun s$$v$$ su i$$ermektedir$.$ Rezervuarkuyusunun $$k$$ noktas$$ndaki $(2)$ bas$$n$,700$kPa de$$erindedir ve s$$cak su$,$ rezervuar$$n alt k$$sm$$ndan $(1)$ yery$$z$$ne $$k$$ yapt$$ kuyunun $$k$$ noktas$$na $(2)$kadar izentropik olarakta$$nmaktad$$r$.$ Fla$$ ay$$rma $$nitesine $(3)$ giren buhar$/$s$$v$$ kar$$m$,$ bu$$nitede izentalpik olarak$270$ kPa bas$$n$$ de$$erine kadar genletirilmekte ve bu genle$$me sonucu olu$$an buhar fraksiyonu $(5),$ bir t$$rbin $$nitesini $$al$$t$$rmaktad$$r$.$ T$$rbin $$nitesinden $$kan ve bas$$n$$ de$$eri$15\mathrm{.}76$kPa olan ak$$m $(6),$ bir yo$$unla$$t$$r$$c$$niteye girmekte ve bu $$niteyi$,15\mathrm{.}76$kPa bas$$n$$tadoygun s$$v$$ su olarak terk etmektedir $(7).$ Bu proses i$$in olan d$$n$$m verimini, bir ba$$kadeyi$$le$,$ t$$rbinde $$retilen g$$ miktar$$n$$n$,$ jeotermal kuyunun $$k$$noktas$$ndaki $(2)$ ak$$kan$$nsahip oldu$$u toplam kullan$$labilir g$$ miktar$$na oran$$n$$ belirleyiniz. T$$rbin $$nitesinin$,$izentropik olarak $$al$$t$$n$$ kabul ediniz.