Virginia Commonwealth University VCU Scholars Compass Theses and Dissertations Graduate School 2014 Optimal design of geothermal power plants Joshua Clarke Virginia Commonwealth University Follow this and additional works at: https://scholarscompass.edu/etd Part of the Energy Systems Commons © The Author Downloaded from https://scholarscompass.edu/etd/3472 This Dissertation is brought to you for free and open access by the Graduate School at VCU Scholars Compass. It has been accepted for inclusion in Theses and Dissertations by an authorized administrator of VCU Scholars Compass. For more information, please contact libcompass@vcu. Optimal design of geothermal power plants A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at Virginia Commonwealth University by Joshua Geiger Clarke B.
Aerospace Engineering, Georgia Institute of Technology, 2002 M. Mechanical and Nuclear Engineering, Virginia Commonwealth University, 2011 Director: Dr. Associate Professor, Mechanical and Nuclear Engineering ©2014 Joshua Clarke Virginia Commonwealth University Richmond, Virginia May 2014 ii Contents List of Figures v List of Tables viii Abstract x 1 Introduction 1 2 Objectives 9 2.1 Geothermal power plants .2 Double-flash plants .1 Geothermal power plants .2 Other power plants of interest .3 Summary and basis for new research. 21 4 Double-flash design space 26 4.4 Results and discussion .1 Constrained design space .2 Optimum specific work output.
45 iii 5 Binary design space 48 5.4 Inputs and constants .4 Results and discussion .1 Constrained design space .2 Optimum specific work output .3 Effect of constrained re-injection temperature. 75 6 Heuristic algorithm selection 79 6.2 Simulated binary crossover .3 Parameter-based mutation .5 Particle swarm optimization .1 Optimum objective function .7 Sensitivity to algorithm control parameters .8 Algorithm validation for binary power plant. 99 7 Effect of climate on plant performance 102 7.2 Air-cooled condensers .1 Principles of operation .1 Typical meteorological year data .2 Climates of interest .4 Impact on plant performance .1 Effect of condenser temperature on turbine efficiency .2 Effect of ambient temperature on specific work output .3 Effect of condenser temperature on plant operations .4 Inputs and constants .7 Results and discussion. 122 8 Binary plant multi-objective optimization 124 8.4 Multi-objective particle swarm optimization .5 Inputs and constants .4 Results and discussion.
153 9 Optimal plant design 155 9.2 Basic binary plant vs.3 Binary plant with superheater and recuperator vs.1 Multi-objective double-flash plant model .2 Pareto-optimal front .3 Maximum specific work output. 180 10 Conclusions 182 Bibliography 185 Vita 192 v List of Figures 1.1 Geothermal power plant .2 Worldwide installed geothermal electric capacity .3 Double flash geothermal power plant .4 Binary geothermal power plant .1 Scope of existing literature .2 Scope of this work compared to existing literature: double-flash plants .3 Scope of this work compared to existing literature: binary plants .1 Double flash geothermal power plant model .2 Double flash temperature entropy diagram .3 Equilibrium solubility of quartz and amorphous silica .4 Constrained design space: Contours of specific work output, w [kJ/kg], vs. T2 and T6 ; Tbrine = 260 o C and Tcond = 30 o C .5 Constrained design space: Contours of specific work output, w [kJ/kg], vs. T2 and T6 , with woptimum indicated by a triangle; Tbrine = 200 − 240 o C, Tcond = 30 − 60 o C 41 4.6 Constrained design space: Contours of specific work output, w [kJ/kg], vs.
T2 and T6 , with woptimum indicated by a triangle; Tbrine = 260 − 300 o C, Tcond = 30 − 60 o C 42 4.7 Optimum specific work output vs. brine temperature at Tcond = 30 − 60 o C .8 Constrained design space for relaxed silica constraint .9 Optimum specific work output vs. brine temperature for two different silica con- straints at Tcond = 30 − 60 o C .1 Binary power plant schematic .2 Binary power plant temperature-entropy diagram .3 Equilibrium solubility of quartz and amorphous silica .4 Constrained design space: Tbrine = 120o C, Tcond = 20o C .5 Effect of increasing condenser temperature; Constrained design space: Tbrine = 120o C, Tcond = 40o C .6 Effect of increasing brine temperature; Constrained design space: Tbrine = 180o C, Tcond = 20o C .7 Effect of increasing brine and condenser temperature; Constrained design space: Tbrine = 180o C, Tcond = 40o C .8 Condenser temperature affects optimum working fluid .9 Constrained design space: Normalized specific work output (w/woptimum ) vs. Tevap /Tcrit and working fluid, with woptimum indicated by a triangle; Tbrine = 80 − 120o C, Tcond = 30 − 60o C .10 Constrained design space: Normalized specific work output (w/woptimum ) vs.
Tevap /Tcrit and working fluid, with woptimum indicated by a triangle; Tbrine = 140 − 180o C, Tcond = 30 − 60o C .11 Optimum working fluid and specific work output: Tbrine = 70 − 200o C, Tcond = 10 − 60o C .12 Optimum working fluid and specific work output: Tbrine = 70 − 200o C, Tcond = 10 − 60o C, Tin j,min = 70o C .13 Optimum specific work output with and without re-injection temperature con- straint: Tbrine = 70 − 200o C, Tcond = 10 − 60o C .1 Double-flash geothermal power plant model .2 Genetic algorithm decision variable progression. White circles indicate infeasible solutions, gray to black are feasible with increasing value of w.3 Particle swarm optimization decision variable progression. White circles indicate infeasible solutions, gray to black are feasible with increasing value of w.4 GA objective function progression .5 PSO objective function progression .1 Air-cooled condenser .2 Condenser temperature vs. dry-bulb temperature for an air-cooled condenser .3 Hourly dry-bulb temperature from Santa Rosa, CA TMY3 data .4 Representative annual profile of hourly dry-bulb temperature data for Santa Rosa, CA.
climates of interest .6 Dry-bulb temperature data for 8 U. climates of interest .7 Semi-qualitative example of turbine efficiency vs.8 Specific work output of an example plant vs. dry-bulb temperature .9 Example unmodified annual hourly condenser temperature profile .10 Example annual hourly profile indicating feasible and infeasible condenser tem- peratures .11 Example modified annual hourly condenser temperature profile .12 Annual hourly dry-bulb temperature profile: Fairbanks, AK .13 Annual hourly dry-bulb temperature profile: Medford, OR .14 Annual hourly dry-bulb temperature profile: Imperial, CA .15 Annual hourly dry-bulb temperature profile: Honolulu, HI .1 Binary power plant with superheater and recuperator schematic .2 Binary power plant with superheater and recuperator temperature-entropy diagram 127 8.3 Swarm of objective vectors and Pareto-optimal front: Tbrine = 160o C, Tdry = 15o C .4 Pareto-optimal front: Tbrine = 160o C, Tdry = 15o C .5 Power output per heat exchanger area: Tbrine = 160o C, Tdry = 15o C .6 Pareto-optimal front with various Tin j,min constraints: Tbrine = 160o C, Tdry = 15o C .7 Pareto-optimal front with various Tin j,min constraints: Tbrine = 80 − 120o C, Tdry = 5 − 25o C .8 Pareto-optimal front with various Tin j,min constraints: Tbrine = 140 − 180o C, Tdry = 5 − 25o C .1 Optimum specific work output vs. brine temperature for double-flash and basic binary plants at Tcond = 10 − 60 o C; no re-injection temperature constraint .2 Optimum specific work output vs.
brine temperature for double-flash and basic binary plants at Tcond = 10 − 60 o C; Tin j,Min = 70 o C .3 Pareto-optimal front binary and double-flash: Tbrine = 160o C, Tdry = 15o C .4 Pareto-optimal front binary and double-flash: Tbrine = 80 − 120o C, Tdry = 5 − 25o C 163 9.5 Pareto-optimal front binary and double-flash: Tbrine = 140 − 180o C, Tdry = 5 − 25o C164 9.6 Pareto-optimal front binary and double-flash: Tbrine = 200 − 240o C, Tdry = 5 − 25o C165 9.7 Pareto-optimal front binary and double-flash: Tbrine = 260 − 300o C, Tdry = 5 − 25o C166 9.8 Maximum specific work output, binary and double-flash: Tbrine = 80 − 300o C, Tdry = 5o C .9 Maximum specific work output, binary and double-flash: Tbrine = 80 − 300o C, Tdry = 15o C .10 Maximum specific work output, binary and double-flash: Tbrine = 80 − 300o C, Tdry = 25o C. 179 viii List of Tables 1.1 Comparison of gaseous emissions from typical power plants .2 Comparison of land requirements for typical power plants .1 Double-flash power plant optimization literature review .2 Binary power plant optimization literature review .1 Double-flash power plant optimization literature review .2 Double-flash power plant model validation .1 Binary power plant optimization literature review .2 Binary power plant model validation .3 Binary power plant potential working fluids .4 Binary power plant model inputs and constants .5 Binary power plant optimum decision variables .1 Number of runs (of 30) converged within ε of highest achieved objective function value and optimum objective function value (w) statistics .2 Median radius of convergence .3 Computational runtime for 300 objective function evaluations and median number of objective function evaluations required to converge within δ of highest known objective function value .4 Number of runs (of 30) converged within ε of highest achieved objective function value for varying GA control parameters .5 Number of runs (of 30) converged within ε of highest achieved objective function value for varying PSO control parameters .6 Comparison of algorithm control parameter cases: t-test results .7 Particle swarm optimization validation .1 Air-cooled condenser energy ratio .2 Binary power plant model inputs and constants .3 Effect of utilizing annual hourly condenser temperature profile vs. annual mean condenser temperature on optimum annual average specific work output .1 Binary power plant model decision variables; multi-objective optimization .2 Binary power plant model inputs and constants; multi-objective optimization .3 Optimal plant design for maximizing specific work output: Binary with no Tin j constraint; Tdry = 5 − 25 o C, Tbrine = 80 − 180 o C .4 Optimal plant design for maximizing specific work output: Binary with Tin j,min = 70 o C; Tdry = 5 − 25 o C, Tbrine = 100 − 180 o C .5 Optimal plant design for maximizing specific work output: Binary with Tin j,min = 90 o C; Tdry = 5 − 25 o C, Tbrine = 120 − 180 o C .6 Optimal plant design at ≈ 0.8 · wmax : Binary with no Tin j constraint; Tdry = 5 − 25 o C, T o brine = 80 − 180 C .7 Optimal plant design at ≈ 0.8 · wmax : Binary with Tin j,min = 70 o C; Tdry = 5 − 25 o C, T o brine = 100 − 180 C .8 Optimal plant design at ≈ 0.8 · wmax : Binary with Tin j,min = 90 o C; Tdry = 5 − 25 o C, T o brine = 120 − 180 C .1 Optimal plant design for maximizing specific work output: Binary with no Tin j constraint; Tdry = 5 − 25 o C, Tbrine = 80 − 300 o C .2 Optimal plant design for maximizing specific work output: Binary with Tin j,min = 70 o C; Tdry = 5 − 25 o C, Tbrine = 100 − 300 o C .3 Optimal plant design for maximizing specific work output: Binary with Tin j,min = 90 o C; Tdry = 5 − 25 o C, Tbrine = 120 − 300 o C .4 Optimal plant design for maximizing specific work output: Double-flash; Tdry = 5 − 25 o C, Tbrine = 120 − 300 o C .5 Optimal plant design at ≈ 0.8 · wmax : Binary with no Tin j constraint; Tdry = 5 − 25 o C, T o brine = 80 − 300 C .6 Optimal plant design at ≈ 0.8 · wmax : Binary with Tin j,min = 70 o C; Tdry = 5 − 25 o C, T o brine = 100 − 300 C .7 Optimal plant design at ≈ 0.8 · wmax : Binary with Tin j,min = 90 o C; Tdry = 5 − 25 o C, T o brine = 120 − 300 C .