SIXTH FRAMEWORK PROGRAMME, PRIORITY 1.6 «Sustainable energy systems» Project : : ENhanced ENhanced Geotherm al Geotherm al I nnovative I nnovative Netw ork Netw ork for for Europe Europe Project ENGI NE ENGI NE Potsdam, 12 January 2007, ENGINE Mid- Potsdam, 12 January 2007, ENGINE Mid -term Conference term Conference POW ER EXTRACTI ON FROM POW ER EXTRACTI ON FROM HDR SYSTEMS HDR SYSTEMS Evald Shpilrain, Oleg Popel, Semen Frid I nstitute for High Tem peratures of the Russian Academ y of Sciences es I nstitute for High Tem peratures of the Russian Academ y of Scienc
T W , kg/s T 1 Scheme of HDR Scheme of HDR T System System WM dq T dl Water T, P T wm P wm Water HE HE T 0 1 = O 150 T C T 0 Air P 1 = 10 bar ( ) kW S = − = N c T T 420 0 = = O T 50 C G 1 kg / s th pw 1 0 kg s ⎛ − ⎞ ⎛ − ⎞ T T ⎜ ⎟ ⎜ ⎟ = = ⋅ ⋅ dl dq 1 0 c dT 1 0 ⎜ ⎟ ⎜ ⎟ pw ⎝ ⎠ ⎝ ⎠ T T 1 1 ⎛ − ⎞ ⎡ ⎤ ⎛ ⎞ − T T ( ) T 1 T T T ⎜ ⎟ = ∫ = − − ⋅ = ⎜ ⎟ − + ⎢ ⎥ l c dT 1 0 c T T c T ln 1 0 1 0 ⎜ ⎟ N th 1 ln 1 ⎜ ⎟ − pw pw 1 0 pw 0 ⎝ ⎠ ⎝ ⎠ ⎣ T T T ⎦ T T 1 0 0 T 0 1 0 T = = x 0 3 , 23 − T T 1 0 ⎡ ⎤ ⎛ ⎞ 1 ( ) = − + = − ≈ ⎜ ⎟ l N ⎢ 1 x ln 1 ⎥ N 1 0 , 872 0 , 128 N th th th ⎝ ⎠ ⎣ ⎦ x l η = = 12 , 8 % max N th
The thermal power of the water flow is transmitted to a working media ( W M ). The optimal thermodynamic cycle should have the heat admission curve (in most cases an isobar) which shape is similar to the water cooling down curve shape: constant heat capacity along the heat admission isobar. T Since generally C pw m ≠ C pw , the specific W M flow rate in the heat exchanger should be q 1 W = C pw / C pw m The specific work l , kJ/ kg of the WM cycle is l = q 1 × η t S Hence the total installation power N [ kW] = l [ kJ/ kg] × W [ kg/ s] In a real cycle C pw m ≠ const , there arises a problem with W M flow rate.
SUBCRITICAL RANKINE CYCLE SUBCRITICAL RANKINE CYCLE T T 1 4 = − q ( kJ / kg ) ( h h ) 1 4 1 P = − ( / ) ( ) l kJ kg h h 4 5 η = = − − 2 / ( ) /( ) l q h h h h T 3 t 1 4 5 4 1 ) T 0 ( P s T 0 5 1 S
TEMPERATURE PINCH EFFECT TEMPERATURE PINCH EFFECT IN HEAT EXCHANGER IN HEAT EXCHANGER T wm , W, kg/s T, var T 0, , var T 1 , 1 kg/s T T 1 T 0 T T s W<W pinch W<W pinch T wm x
TEMPERATURE PINCH EFFECT TEMPERATURE PINCH EFFECT IN HEAT EXCHANGER IN HEAT EXCHANGER T wm , W, kg/s T, var T 0, , var T 1 , 1 kg/s T T 1 T 0 T T s W<W pinch W<W pinch T wm x
TEMPERATURE PINCH EFFECT TEMPERATURE PINCH EFFECT IN HEAT EXCHANGER IN HEAT EXCHANGER T wm , W, kg/s T, var T 0, , var T 1 , 1 kg/s T T 1 T 0 T T s W<W pinch W<W pinch T wm x
TEMPERATURE PINCH EFFECT TEMPERATURE PINCH EFFECT IN HEAT EXCHANGER IN HEAT EXCHANGER T wm , W, kg/s T, var T 0, , var T 1 , 1 kg/s T T 1 T 0 T T s W<W pinch W<W pinch T wm x
TEMPERATURE PINCH EFFECT TEMPERATURE PINCH EFFECT IN HEAT EXCHANGER IN HEAT EXCHANGER T wm , W, kg/s T, var T 0, , var T 1 , 1 kg/s T T 1 T T 0 T s W<W pinch W<W pinch T wm x
TEMPERATURE PINCH EFFECT TEMPERATURE PINCH EFFECT IN HEAT EXCHANGER IN HEAT EXCHANGER T wm , W, kg/s T, var T 0, , var T 1 , 1 kg/s T T 1 T T 0 T s W<W pinch W<W pinch T wm x
TEMPERATURE PINCH EFFECT TEMPERATURE PINCH EFFECT IN HEAT EXCHANGER IN HEAT EXCHANGER T wm , W, kg/s T, var T 0, , var T 1 , 1 kg/s T T 1 T T 0 T s W<W pinch W<W pinch T wm x
TEMPERATURE PINCH EFFECT TEMPERATURE PINCH EFFECT IN HEAT EXCHANGER IN HEAT EXCHANGER T wm , W, kg/s T, var T 0, , var T 1 , 1 kg/s T T 1 T T 0 T s W<W pinch W<W pinch T wm x
TEMPERATURE PINCH EFFECT TEMPERATURE PINCH EFFECT IN HEAT EXCHANGER IN HEAT EXCHANGER T wm , W, kg/s T, var T 0, , var T 1 , 1 kg/s T T 1 T T 0 T s W<W pinch W<W pinch T wm x
TEMPERATURE PINCH EFFECT TEMPERATURE PINCH EFFECT IN HEAT EXCHANGER IN HEAT EXCHANGER T wm , W, kg/s T, var T 0, , var T 1 , 1 kg/s T T 1 T T 0 T s W<W pinch W<W pinch T wm x
TEMPERATURE PINCH EFFECT TEMPERATURE PINCH EFFECT IN HEAT EXCHANGER IN HEAT EXCHANGER T wm , W, kg/s T, var T 0, , var T 1 , 1 kg/s T T 1 T T 0 T s W<W pinch W<W pinch T wm x
TEMPERATURE PINCH EFFECT TEMPERATURE PINCH EFFECT IN HEAT EXCHANGER IN HEAT EXCHANGER T wm , W, kg/s T, var T 0, , var T 1 , 1 kg/s T T 1 T T 0 T s W<W pinch W<W pinch T wm x
TEMPERATURE PINCH EFFECT TEMPERATURE PINCH EFFECT IN HEAT EXCHANGER IN HEAT EXCHANGER T wm , W, kg/s T, var T 0, , var T 1 , 1 kg/s T T 1 T T 0 T s W<W pinch W<W pinch T wm x
TEMPERATURE PINCH EFFECT TEMPERATURE PINCH EFFECT IN HEAT EXCHANGER IN HEAT EXCHANGER T wm , W, kg/s T, var T 0, , var T 1 , 1 kg/s T T 1 T T 0 T s W<W pinch W<W pinch T wm x
TEMPERATURE PINCH EFFECT TEMPERATURE PINCH EFFECT IN HEAT EXCHANGER IN HEAT EXCHANGER T wm , W, kg/s T, var T 0, , var T 1 , 1 kg/s T T 1 T T 0 T s W<W pinch W<W pinch T wm x
TEMPERATURE PINCH EFFECT TEMPERATURE PINCH EFFECT IN HEAT EXCHANGER IN HEAT EXCHANGER T wm , W, kg/s T, var T 0, , var T 1 , 1 kg/s T T 1 T T 0 T s W<W pinch W<W pinch T wm x
TEMPERATURE PINCH EFFECT TEMPERATURE PINCH EFFECT IN HEAT EXCHANGER IN HEAT EXCHANGER T wm , W, kg/s T, var T 0, , var T 1 , 1 kg/s T T 1 T T 0 T s W<W pinch W<W pinch T wm x
TEMPERATURE PINCH EFFECT TEMPERATURE PINCH EFFECT IN HEAT EXCHANGER IN HEAT EXCHANGER T wm , W, kg/s T, var T 0, , var T 1 , 1 kg/s T T 1 T T 0 T s W<W pinch W<W pinch T wm x
TEMPERATURE PINCH EFFECT TEMPERATURE PINCH EFFECT IN HEAT EXCHANGER IN HEAT EXCHANGER T wm , W, kg/s T, var T 0, , var T 1 , 1 kg/s T T 1 T T 0 T s W<W pinch W<W pinch T wm x
TEMPERATURE PINCH EFFECT TEMPERATURE PINCH EFFECT IN HEAT EXCHANGER IN HEAT EXCHANGER T wm , W, kg/s T, var T 0, , var T 1 , 1 kg/s T T 1 T T 0 T s W<W pinch W<W pinch T wm x
TEMPERATURE PINCH EFFECT TEMPERATURE PINCH EFFECT IN HEAT EXCHANGER IN HEAT EXCHANGER T wm , W, kg/s T, var T 0, , var T 1 , 1 kg/s T T 1 T T 0 T s W<W pinch W<W pinch T wm x
TEMPERATURE PINCH EFFECT TEMPERATURE PINCH EFFECT IN HEAT EXCHANGER IN HEAT EXCHANGER T wm , W, kg/s T, var T 0, , var T 1 , 1 kg/s T T 1 T T s T 0 W<W pinch W<W pinch T wm x
TEMPERATURE PINCH EFFECT TEMPERATURE PINCH EFFECT IN HEAT EXCHANGER IN HEAT EXCHANGER T wm , W, kg/s T, var T 0, , var T 1 , 1 kg/s T T 1 T T s T 0 W<W pinch W<W pinch T wm x
TEMPERATURE PINCH EFFECT TEMPERATURE PINCH EFFECT IN HEAT EXCHANGER IN HEAT EXCHANGER T wm , W, kg/s T, var T 0, , var T 1 , 1 kg/s T T 1 T T s T 0 W<W pinch W<W pinch T wm x
TEMPERATURE PINCH EFFECT TEMPERATURE PINCH EFFECT IN HEAT EXCHANGER IN HEAT EXCHANGER T wm , W, kg/s T, var T 0, , var T 1 , 1 kg/s T T 1 T T s T 0 W=W pinch W=W pinch T wm x
TEMPERATURE PINCH EFFECT TEMPERATURE PINCH EFFECT IN HEAT EXCHANGER IN HEAT EXCHANGER T wm , W, kg/s T, var T 0, , var T 1 , 1 kg/s T T 1 T T s T 0 W>W pinch W>W pinch T wm x
TEMPERATURE PINCH EFFECT TEMPERATURE PINCH EFFECT IN HEAT EXCHANGER IN HEAT EXCHANGER T wm , W, kg/s T, var T 0, , var T 1 , 1 kg/s T T 1 T T s T 0 W>W pinch W>W pinch T wm x
TEMPERATURE PINCH EFFECT TEMPERATURE PINCH EFFECT IN HEAT EXCHANGER IN HEAT EXCHANGER T wm , W, kg/s T, var T 0, , var T 1 , 1 kg/s T T 1 T T s T 0 W>W pinch W>W pinch T wm x
TEMPERATURE PINCH EFFECT TEMPERATURE PINCH EFFECT IN HEAT EXCHANGER IN HEAT EXCHANGER T wm , W, kg/s T, var T 0, , var T 1 , 1 kg/s T T 1 T T s T 0 W>W pinch W>W pinch T wm x
EFFICIENCY VERSUS FLOW- -RATE RATE EFFICIENCY VERSUS FLOW T T 1 T 1 η t T pinch q × W η = η 1 T 0 t N η th T 0 W pinch W
150 P c = 4.264 MPa C 3 H 8 O C T c = 96.8 O C 100 T, 4.264 4.2 4.2 4.1 4.1 4 4 3.9 3.9 3.8 3.8 3.7 3.7 3.6 3.6 3.5 3.5 3.4 3.4 3.3 3.3 3.2 3.2 3.1 3.1 3 3 2.9 2.9 2.8 2.8 2.7 2.7 2.6 2.6 2.5 2.5 2.4 2.4 2.3 2.3 2.2 2.2 2.1 2.1 2 2 1.9 1.9 50 1.8 1.8 4,5 5,0 5,5 6,0 S, kJ/kgK
150 P c = 3.647 MPa IC 4 H 10 O C T c = 134.9 3.6 3.647 3.6 3.5 3.5 3.4 3.4 3.3 3.3 3.2 3.2 3.1 3.1 3 3 2.9 2.9 2.8 2.8 2.7 2.7 2.6 2.6 2.5 2.5 2.4 2.4 2.3 2.3 2.2 2.2 2.1 2.1 O C 2 2 100 1.9 1.9 1.8 1.8 T, 1.7 1.7 1.6 1.6 1.5 1.5 1.4 1.4 1.3 1.3 1.2 1.2 1.1 1.1 1 1 0.9 0.9 0.8 0.8 0.7 0.7 50 3,5 4,0 4,5 5,0 5,5 S, kJ/kgK
CONCLUSIONS: CONCLUSIONS: 1. There exist a thermodynamic limit of installation efficiency, defined by the outlet temperature of geothermal water; 2. An optimal thermodynamic cycle should have the heat admission curve similar to the cooling down curve of geothermal water; 3. This condition can be realized with a supercritical Rankine cycle; 4. To provide for maximum installation efficiency it is not enough to maximize the cycle thermal efficiency. It is necessary to look for maximum of the η t W product; 5. The optimal working media flow rate is governed by the temperature pinch in the heat exchanger.
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