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Geothermal Binary Rankine Cycles
Abstract
This report is for a LOW-BIN (Efficient Low Temperature Geothermal project. The main objective is to study and recommend specific optimal Rankine cycles using water as the primary source of heat. The water is at a temperature of 1600C. This Rankine cycle is using R134 as working fluid for the geothermal power machine. This project is supposed to generate electricity from low temperature resources with profitable operation down up to around 600C. The main Rankine Cycle parameters and components are idealized. This is as found in the shell, the tube condenser and the heat exchanger.
Introduction
The main objectives of this project are
- Specify suitable temperature and pressures for the cycle
- Determine the thermal efficiency of a reasonable pump, turbine efficiencies and pressure drops.
- Optimize the cycle performance by varying the pressures and temperatures
The refrigerant used, R134a was selected because of the following reasons
- It is excellent in cooling the heat pumps in industries which involve Rankine cycle machines
- This type of refrigerant is readily available in the market
The main components of Rankine cycle parameters have been defined in the schematic diagram below.
MODELING RANKINE CYCLE PARAMETERS
Heat exchanger
Condenser (cooling heat exchanger)
This is a standard practice in a geothermal binary power plants and the equation for the heat exchange is given by the following equation.
U0 = A
Where A0 and Ai represents the outside and inside surfaces of the tubes respectively. The heat transfer coefficient inside the tube is given the parameter hi where the refrigerant flows through; h0 is the heat transfer coefficient outside the tubes of the condenser and thermal conductivity of the tubes is given by the coefficient constant, k.
The heat transfer coefficient outside the tubes is dependent on the following equation for laminar film condensation on horizontal tubes.
h0 = 0.725
The constants ρ and ρv represents the density of the working fluid in liquid and vapor forms respectively. hfg is the latent heat uf the working fluid, kf is the tghermal conductivity of the fluid, d is the diameter of thetube measured from the outside, Tg the saturation temperature of the wall of the tube.
The heat transfer coefficient inside the tubes for turbulence is give by the formula below
hi = Nuk/D
Nu = 0.0023Re0.8Pr0.4
Re = u*D* ρ / µ
D is outside diameter of the tube, k is thermal conductivity, Nu is the Nusselt number, Pr the Prant number, Re is the Reynolds number calculated for the p µ of the water properties
Heat Exchanger the evaporator
The plate heat exchanger is corrugated parallel plates attached to one another and then fitted into a casing. The overall heat-transfer coefficient is given by
U0 = 1÷ [1/hwf + Δx/ktit + 1/hgw]
The parameters Δx is the plate thichkness, hwf is the heat transfer coefficient of the fluid, hgw is the heat transfer coefficient of the ground water and k the thermal conductivity of the plate’s material.
Rankine cycle optimization for different working fluids
Using EASY tool developed by the Parallel CFD and Optimization the work becomes easier. To optimize the Rankine Cycle for a typical geothermal power the variables, limits of the variables and the objectives need to be defined.
Optimization objectives
For net conversion efficiency of the plant, maximization is given by
hcycle = Wturbine – Npump ÷ Qheatexch = (h4 – h5)*mwf - Npump ÷ (h3 –h2)*mwf
Variables of optimization
Pressure of the liquid working fluid
Ground water mass flow rate
Temperature difference
Temperature difference cooling fluid
Temperature threshold at 650C R134a
Optimization variables are shown in the figure below
A representative solution for R134a
Feature of heat exchangers and dimensions
The optimal solutions – R134a
Rankine cycle variables for the selected optimal solutions for the machine and R134a as working fluid
Obsreve the significant mass flow rate difference of the working fluid and the pump power (14kW to 60kW). Conversely, the cooling fluid flow needed for the condenser is much less. The ground water reaches 1200C implying that due to the high temperatures of the water and the condenser fluid.
Comparison with existing binary machines optimized for 1000C geothermal water
Rankine cycle variables for selected optimal solutions
Work cited
Kontoleontos E, mendrinos D. 2010. Optimized geothermal binary power cycles. Retrived from
http://www.lowbin.eu/public/CRES-Optimized%20geothermal%20binary%20power%20cycles.pdf
Franco A. Villani M. 2010. Optimal design of binary cycle power plants for water-dominated, medium-temperature geothermal fields. Retrieved from http://eprints.adm.unipi.it/663/1/Versione_UNIPRINTS.pdf
Geo Heat center. 2010. Small geothermal projects examples- geo-het center. Retrieved from geoheat.oit.edu/bulletin/bull20-2/art2.pdf
