Exercise 1. (session: )

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1 EEN-E3001, FUNDAMENTALS IN INDUSTRIAL ENERGY ENGINEERING Exercise 1 (session: ) Problem 3 will be graded. The deadline for the return is on at 12:00 am (before the exercise session). You can hand in your answer either into the brown mail box in K1 building next to the room 148, or straight to the course assistant before the next session ( return also possible). Problem 1 A plant s process has a heat demand of 12 MW. The heat is taken from the steam network, where the pressure of the steam is 14 bar and temperature 580 K. The pressure level in the process is 4 bar. So, before entering the process, the steam flows through a reduction valve. What is the temperature of the steam after the valve and what is the flow rate of the steam into the process [kg/s]? Tehtävä 1 Tehdas ottaa tarvitsemansa 12 MW:n lämpötehon höyryverkosta, jossa höyryn paine on 14 bar ja lämpötila 580 K Höyry otetaan prosessiin reduktioventtiilin kautta. Prosessin painetaso on 4 bar. Mikä on höyryn lämpötila reduktioventtiilin jälkeen ja mikä on höyryn massavirta prosessiin? Solution: The enthalpy of the steam remains unchanged over the reduction valve. The enthalpy is found out from the h,s-drawing: h 1 = h 2 = h(14 bar, 580 K) = 3055 /kg Also the temperature of the steam in point 2 is received from the h,s-drawing, when moving from point 1 along the constant enthalpy line to the pressure level p 2 = 4 bar; T 2 = T(p 2, h 1) = 295 C. We assume that the condensate leaves the process as saturated water. Then, the enthalpy of the water is found out from the saturated water and steam-drawing: h 3 = h (4 bar) = 605 /kg The mass flow of the steam is calculated using the energy balance: 1

2 Φ Process = m 3 h Process m 3 = Φ Process h 2 h 3 = kw = 4,90 kg s Problem 2 The power plant of a mill (Figure 1) generates electricity and heat for processes in the mill. The steam before the superheaters has 1 % wetness and 40 bar pressure. The mass flow of the steam is 15 kg/s. The temperature of the steam rises with 200 C in the superheaters. Bled steam in the pressure of 16 bar is taken from the turbine for process A. The process A uses a thermal power of 20 MW from the steam, and the returning water is assumed to be saturated (16 bar). The steam for the process B is in 4 bar pressure, but it has to be cooled down to 180 C with spray water. The spray water is saturated and in 4 bar pressure. The isentropic efficiency of the steam turbine is 65%. a) What is the enthalpy of the steam at points 1 and 2? b) How much spray water has to be injected into the steam for process B (m 6, kg/s)? Tehtävä 2 Erään tehtaan voimalaitos (Figure 1) tuottaa sähköä ja lämpöä tehtaan prosesseja varten. Höyrykattilan tulistimiin menevän höyryn kosteus on 1 %, paine 40 bar ja massavirta 15 kg/s. Tulistimissa höyryn lämpötila nousee 200 C. Prosessia A varten otetaan turbiinista väliottohöyryä paineessa 16 bar. Prosessin A ottama lämpöteho höyrystä on 20 MW, ja siitä palautuva vesi voidaan olettaa olevan kylläisessä tilassa (16 bar). Prosessiin B menevä höyry on paineessa 4 bar, mutta se on jäähdytettävä ruiskutusvedellä 180 C:een lämpötilaan. Ruiskutusvesi on 4 bar paineista kylläistä vettä. Höyryturbiinin isentrooppinen hyötysuhde on 65%. a) Mitkä ovat höyryn entalpiat pisteissä 1 ja 2? b) Kuinka paljon vettä on ruiskutettava prosessiin B menevän höyryn sekaan (m 6, kg/s)? Figure 1. The flow chart of the process in problem 2. 2

3 Solution: a) Enthalpies of saturated water and steam at point 1: h (40 bar) = 1088 /kg h (40 bar) = 2801 /kg h 1 = x h 1 + (1 x) h 1 h 1 = 0, (1 0,99) 1088 = 2783,9 kg Temperature of the saturated steam at 40 bar: t 1 (40 bar) 250 C Temperature increases with 200 C in the superheaters t 2 = = 450 C Enthalpy of steam in point 2 can be looked from h,s-diagram: h 2(40 bar, 450 C) = 3330 /kg b) Bleed steam, isentropic decrease in pressure h 3s(16 bar) = /kg isentropic efficiency of 65%: h 3 = h 2 η s (h 2 h 3s ) h 3 = ,65 ( ) h 4 = h (16 bar) = 855 /kg = kg Mass flow of the bleed steam is calculated from the energy balance of the process A: m 3h 3 = m 3h 4 + P A m 3 = P A = kw = 8,673 kg/s (h 3 h 4 ) ( )/kg Enthalpy of back-pressure steam (40 bar -> 4 bar): h 5s = 2760 /kg h 5 = h 2 η s (h 2 h 5s ) h 5 = ,65 ( ) = 2 959,5 kg Temperature of steam in point 5 can be looked from h,s-diagram: t C Enthalpies at points 6 and 7: 3

4 h 6 = h (4 bar) = 605 /kg h 7 = h(4 bar, 180 C) = 2820 /kg m 5 = m 2 m 3 = 15 8,673 = 6,327 kg/s Mass flow of the spray water is calculated according to the energy and mass balances: h 5 m 5 + h 6 m 6 = h 7 m 7 m 7 = m 5 + m 6 h 5 m 5 + h 6 m 6 = h 7 m 5 + h 7 m 6 m 6 = m 5(h 7 h 5 ) h 6 h 7 = 6,327 ( ,5) = 0,398 kg/s Problem 3 * Steam (80 bar, 520 C) is led to a steam turbine, which has an isentropic efficiency of 70% (See Figure 2). Bleed steam is taken from a turbine at pressure level of 20 bars. The mass flow of the bleed steam is 8 kg/s and it is used to heat a process. The return flow from the process is assumed to be saturated water at the pressure of 20 bars. The water is led into a steam separator, where the pressure is 4 bar. The water from the separator flows to the district heat network of the plant, while the steam from the separator is condensed and the released heat is used to warm up the driving water. All of the water sent to the district heat network is assumed to return in 50 C temperature and 1 bar pressure. a) What is the thermal power used by the process? b) What is the thermal power used by the district heat network? c) What is the thermal power released to the driving water? Tehtävä 3 * Höyryä (80 bar, 520 C) johdetaan höyryturbiiniin, jonka isentrooppinen hyötysuhde on 70% (Figure 2). Turbiinin väliottohöyryn paine on 20 bar. Väliottohöyryn massavirta on 8 kg/s ja sitä käytetään erään prosessin tarpeisiin. Prosessista palautuva vesi on kylläistä vettä 20 bar paineessa. Vesi johdetaan höyrynerottimeen, jonka paine on 4 bar. Höyrynerottimesta poistuva vesi johdetaan tehtaan kaukolämpöverkkoon, ja erottimesta vapautuva höyry lauhdutetaan ja lämpö käytetään käyttöveden lämmittämiseen. Kaikki kaukolämpöverkkoon syötetty vesi oletetaan palaavan tilassa 50 C ja 1 bar. a) Mikä on prosessin käyttämä lämpöteho? b) Mikä on kaukolämpöverkon käyttämä lämpöteho? c) Mikä on käyttöveden lämmitykseen saatava lämpöteho? 4

5 80 bar, 520 C bar bar Condenser DH network Figure 2 Process diagram for problem 3* 5