4.3 Correlations and Component Models in GEOPHIRES
4.3.5 Levelized Cost Models
where W is the amount of heat withdrawn from the geothermal fluid in MWth.
The wellfield O&M costs consist of the remaining 25% of the labor costs and 1% of the total well capital costs, again similar to the correlation in GETEM (DOE, 2012) (in $/year):
CO&M,w f = 0.25 · Clabor+ 1% · Ccap,well. (4.40)
In the case of reservoir temperature drawdown beyond a user-defined threshold, redrilling is required. The capital cost for these wells are modeled as O&M costs by dividing their cost by the lifetime of the plant and adding them to the wellfield O&M costs.
The user has to input the water loss rate occurring in the EGS reservoir. The annual expenses to pay for the make-up water are calculated using a water rate of $660/Ml ($2.5 per 1000 gallons).
All the capital and O&M cost correlations provided in this section come with inherent uncertainties. To address these uncertainties, a sensitivity analysis is performed when evaluating the levelized costs for various EGS scenarios in Section 5.1.
4.3.5
Levelized Cost Models
Three models are available in GEOPHIRES to calculate the levelized cost of electricity (LCOE) or heat (LCOH): (1) the Fixed Charge Rate Model, (2) the Standard Levelized Cost Model, and (3) the BICYCLE Levelized Life Cycle Cost Model.
Chapter 4. GEOPHIRES Simulation Tool 50
Fixed Charge Rate (FCR) Model
The first model is the Fixed Charge Rate (FCR) Model in which the LCOE/LCOH is cal- culated as (Armstead and Tester, 1987):
LCOEor LCOH= FCR· Ccap+ CO&M
E (4.41)
with Ccapthe total capital investment, CO&M the yearly operation and maintenance (O&M) cost and E the average annual electricity output in kWheor direct-use heat generation in
MMBTU. The FCR is a single number, e.g. 12.8% in the National Energy Modeling System (Tester et al., 2006), which is multiplied by the total capital cost to obtain the annual cost of invested capital. The FCR is estimated based on several financial parameters, e.g. debt interest rate, rates of return on equity capital, and tax rates (Armstead and Tester, 1987):
FCR= CRF + f (CRF(i, n), tax credits) (4.42)
with CRF the capital recovery factor. The CRF is the fraction of capital investment that must be paid back every year to fully repay a loan within n years at an interest rate i. It is calculated as (Armstead and Tester, 1987):
CRF(i, n) = i
1− (1 + i)−n. (4.43)
Standard Levelized Cost Model
The second model is the Standard Levelized Cost Model which discounts both expendi- tures and revenues to current day dollars (OECD/IEA, 2010):
LCOEor LCOH = Ccap+ ∑lt t=1 CO&M,t−It (1+i)t ∑n t=1 Et (1+i)t (4.44) with lt being the lifetime of the plant, Ccap the capital investment, and CO&M,t, It and Wt
representing the O&M cost, revenue from heat or electricity sales in CHP mode, and electricity or direct-use heat generation in year t, respectively.
Chapter 4. GEOPHIRES Simulation Tool 51
BICYCLE Levelized Cost Model
The third and most advanced economic model is the BICYCLE Levelized Life Cycle Cost Model developed at Los Alamos National Laboratory (Hardie, 1981). This model assumes that the financing of the EGS project occurs through debt (bonds) and equity and allows for variable debt/equity return rates. The ratio of outstanding debt to outstanding equity remains constant while paying off over the lifetime of the plant. Furthermore, the model takes into account inflation, tax rates and tax credits. The levelized cost is calculated as:
LCOEor LCOH= ∑ NPV lt t=1 Wt·(1+iin f)t (1+iave)t (4.45) where NPV is the net present value, iin f the inflation rate and iave the average return on investment (tax and inflation adjusted), calculated as:
iave= db · idb· (1 − iit)+ eq · ieq (4.46)
with db, eq, idb, iit and ieq the fraction of investment through debt, the fraction of invest- ment through equity (eq= 1 − db), the inflated debt interest rate, income tax rate, and the inflated equity return rate, respectively.
The NPV in Equation (4.45) is calculated as:
NPV = NPVcap+ NPVO&M+ NPVf c + NPVit+ NPVgrt− NPVitc (4.47)
with NPVcap, NPVO&M, NPVf c, NPVit, NPVgrt and NPVitc representing the net present value contribution due to the capital costs, O&M costs, fixed charges, income taxes, gross rev- enue taxes, and investment tax credits. They are calculated as follows:
NPVcap = lt ∑ t=1 ( Ccap· CRF(iave, n) (1+ iave)t ) , (4.48) NPVO&M = lt ∑ t=1 ( CO&M,t· (1 + iin f)t (1+ iave)t ) , (4.49)
Chapter 4. GEOPHIRES Simulation Tool 52 NPVf c = lt ∑ t=1 (
Ccap· ipt· (1 + iin f)t (1+ iave)t ) , (4.50) NPVit= lt ∑ t=1 ( i it 1−iit ) (
Ccap· CRF(iave, lt) − Ccap1lt ) (1+ iave)t , (4.51) NPVgrt = ( igrt 1− igrt )
(NPVcap+ NPVO&M + NPVf c+ NPVit− NPVitc), (4.52)
NPVitc =
Ccap· iitc
1− iit (4.53)
with iit, igrt, ipt, iin f and iitcrepresenting the income tax rate, gross revenue tax rate, property tax rate, inflation rate and investment tax credit rate, respectively. In Equation (4.51), the term (Ccap/lt) represents linear depreciation. Further, the term Ccap represents the overnight capital cost which can be adjusted for inflation during construction.
Which economic model to use depends on how rigorous the economic analysis should be. The BICYCLE model is believed to more closely represent market conditions, but requires a good understanding and knowledge of the different economic parameters. The FCR and Standard Levelized Cost Model on the other hand are easier to understand and to apply but may be less realistic.
References
Armstead, H. C. H. and Tester, J. W. (1987). Heat Mining. E. & F.N. Spon Ltd., London and New York.
Augustine, C. R. (2009). Hydrothermal spallation drilling and advanced energy conversion
technologies for Engineered Geothermal Systems. PhD Dissertation, Massachusetts Institute
of Technology, Cambridge, Massachusetts, United States.
Beckers, K. F., Lukawski, M. Z., Reber, T. J., Anderson, B. J., Moore, M. C., and Tester, J. W. (2013). Introducing GEOPHIRES v1.0: Software Package for Estimating Levelized
Chapter 4. GEOPHIRES Simulation Tool 53 Cost of Electricity and/or Heat from Enhanced Geothermal Systems. In Proceedings
Thirty-Eighth Workshop on Geothermal Reservoir Engineering, Stanford University, Stan-
ford, California, February 11 - February 13, 2013, SGP-TR-198.
Beckers, K. F., Lukawski, M. Z., Anderson, B. J., Moore, M. C., and Tester, J. W. (2014a). Levelized costs of electricity and direct-use heat from Enhanced Geothermal Systems.
Journal of Renewable and Sustainable Energy, 6, 013141.
Beckers, K. F., Lukawski, M. Z., Anderson, B. J., Moore, M. C., and Tester, J. W. (2014b). Erratum: “Levelized costs of electricity and direct-use heat from Enhanced Geothermal Systems” [J. Renewable Sustainable Energy 6, 013141 (2014)]. Journal of Renewable and
Sustainable Energy, 6, 059902.
Beckers, K. F., Lukawski, M. Z., Aguirre, G. A., Hillson, S. D., and Tester, J. W. (2015). Hy- brid Low-Grade Geothermal-Biomass Systems for Direct-Use and Co-Generation: from Campus Demonstration to Nationwide Energy Player. In Proceedings Fortieth Workshop
on Geothermal Reservoir Engineering, Stanford University, Stanford, California, January
26 - January 28, 2015, SGP-TR-204.
DiPippo, R. (2004). Second law assessment of binary plants generating power from low- temperature geothermal fluids. Geothermics, 33 (5): 565–586.
DiPippo, R. (2012). Geothermal power plants: principles, applications, case studies and environ-
mental impact. Butterworth-Heinemann, 3rdedition.
DOE (2012). Geothermal Electricity Technology Evaluation Model (GETEM), Version Au-
gust 2012. U.S. Department of Energy Geothermal Technologies Program. Available
at http://www1.eere.energy.gov/geothermal/getem.html.
Fox, R. W., Pritchard, P. J., and McDonald, A. T. (2004). Introduction to Fluid Mechanics. John Wiley & Sons, 6thedition.
Chapter 4. GEOPHIRES Simulation Tool 54 Gringarten, A. C., Witherspoon, P. A., and Ohnishi, Y. (1975). Theory of heat extraction
from fractured hot dry rock. Journal of Geophysical Research, 80 (8): 1120–1124.
Hardie, R. W. (1981). BICYCLE II: A Computer Code for Calculating Levelized Life-Cycle Costs, LA-89089. Los Alamos National Laboratory, Los Alamos, New Mexico, United States. Heidinger, P., Dornst¨adter, J., and Fabritius, A. (2006). HDR economic modelling: HDRec
software. Geothermics, 35 (5): 683–710.
Hunsbedt, A., Lam, S. T.-F., and Kruger, P. (1984). User’s manual for the one-dimensional
linear heat sweep model. Stanford Geothermal Program, Interdisciplinary Research in En-
gineering and Earth Sciences, Stanford University, Stanford, California, United States. IHS (2013). IHS CERA Power Capital cost Index (PCCI). Available at http://
www.ihs.com/info/cera/ihsindexes/index.aspx.
Johnson, C., Augustine, C., and Goldberg, M. (2012). Jobs and Economic Development Impact
(JEDI) Model Geothermal User Reference Guide, Technical Report NREL/TP-6A20-55781.
National Renewable Energy Laboratory (NREL), Golden, Colorado, United States. Kitsou, O. I., Herzog, H. J., and Tester, J. W. (2000). Economic modeling of HDR enhanced
geothermal systems. In Proceedings World Geothermal Congress 2000, Kyushu - Tohoku, Japan, May 28 - June 10, 2000, pages 3779–3784.
Lukawski, M. Z., Anderson, B. J., Augustine, C., Capuano, L. E., Beckers, K. F., Livesay, B., and Tester, J. W. (2014). Cost analysis of oil, gas, and geothermal well drilling. Journal
of Petroleum Science and Engineering, 118: 1–14.
Lukawski, M. Z. (2016). Comparison of Subcritical and Supercritical Organic Rankine Cycles
(ORC) for Efficient Conversion of Low- and Medium-Temperature Heat to Electricity. Internal
Chapter 4. GEOPHIRES Simulation Tool 55 Mines, G. (2008). Geothermal Electricity Technologies Evaluation Model DOE tool for Assessing Impact of Research on Cost of Power. In Thirty-Third Workshop on Geothermal
Reservoir Engineering, Stanford University, Stanford, California, January 28 - January 30,
2008.
Mines, G. and Nathwani, J. (2013). Estimated power generation costs for EGS. In Pro-
ceedings Thirty-Eighth Workshop on Geothermal Reservoir Engineering, Stanford University,
Stanford, California, February 11 - February 13, 2013, SGP-TR-198.
NAG (2011). NAG Fortran Library Manual - Mark 23. The Numerical Algorithms Group Limited.
OECD/IEA (2010). Projected Costs of Generating Electricity: 2010 Edition. OECD NEA/IEA, Organisation for Economic Co-operation and Development Nuclear Energy Agency / International Energy Agency.
Ramey Jr, H. J. (1962). Wellbore heat transmission. Journal of Petroleum Technology, 14 (04): 427–435.
Reber, T. J. (2013). Evaluating Opportunities for Enhanced Geothermal System-Based District
Heating in New York and Pennsylvania. Master Thesis, Cornell University, Ithaca, New
York, United States.
Reber, T. J., Beckers, K. F., and Tester, J. W. (2014). The transformative potential of geother- mal heating in the US energy market: A regional study of New York and Pennsylvania.
Energy Policy, 70: 30–44.
Tester, J. W. and Herzog, H. J. (1990). Economic Predictions for Heat Mining: A Review and
Analysis of Hot Dry Rock (HDR) Geothermal Energy Technology, Massachusetts Institute
of Technology Energy Laboratory Report MIT-EL 90-001. U.S. Department of Energy, Geothermal Technology Division.
Chapter 4. GEOPHIRES Simulation Tool 56 Tester, J. W., Anderson, B., Batchelor, A., Blackwell, D., DiPippo, R., Drake, E., Garnish, J., Livesay, B., Moore, M. C., Nichols, K., Petty, S., Toksz, M. N., and Veatch Jr., R. W. (2006). The future of geothermal energy: Impact of enhanced geothermal systems (EGS) on the
CHAPTER 5
GEOPHIRES CASE-STUDIES
This chapter presents three case-studies utilizing GEOPHIRES to investigate the tech- nical and economic performance of deep geothermal energy using Enhanced Geother- mal Systems (EGS) for electricity and direct-use heat (Section 5.1), district heating sys- tems (Section 5.2), and cogeneration (Section 5.3). The sections are based on material published in (Beckers et al., 2014a,b), (Reber et al., 2014), and (Beckers et al., 2015), re- spectively. Other published works utilizing GEOPHIRES, not further discussed here, are (Tester et al., 2015a) and (Tester et al., 2015b).