Quantification of Geothermal Resource Risk A Practical Perspective

Transcription

1 GRC Transactions, Vol. 34, 2010 Quantification of Geothermal Resource Risk A Practical Perspective Subir K. Sanyal and James W. Morrow GeothermEx, Inc. Richmond, California Keywords Certainty-equivalent, Kamojang, learning-curve, meritmeasure, portfolio effect, probabilistic study, resource risk, sensitivity study ABSTRACT Quantification of geothermal resource risk is of major importance in the financing of geothermal projects. This paper considers several practical merit measures of geothermal resource risk (potential resource base, drilling success rate, unit capital cost per installed kilowatt, internal rate of return, levelized cost of power and discounted profit-to-investment ratio) and various practical approaches to risk quantification utilizing these merit measures. The risk quantification approaches considered in this paper are: sensitivity studies, probabilistic assessment and certainty-equivalent mapping. Based on such quantification and considering the experience of developers and operators in the geothermal industry, the positive impact of the learning-curve effect and the portfolio effect on resource risk is described. Using certainty-equivalent mapping, the evolution of the resource risk profile of a project through its various phases is illustrated. Certainty-equivalent mapping is shown to be the best overall tool for resource risk quantification. The case history of the Kamojang geothermal field in Indonesia, which has been generating power for 25 years, is invoked to illustrate some of the concepts. Introduction Quantification of geothermal resource risk is important in the financing of geothermal projects; but there is no unique approach to this quantification. Risk can be quantified in a deterministic way through sensitivity studies or can be approached in a probabilistic way to specifically reflect uncertainties. Resource risk can be considered directly; for example, the probability of reserves being proven inadequate for a project or the probability of a well being unsuccessful. Alternatively, resource risk can be quantified indirectly through the cost consequence of the risk; for example, the probability of the levelized power cost exceeding a threshold or the internal rate of return falling below a required minimum. Based on our long experience in the exploration, development and financing of geothermal projects, we have developed various practical approaches to this issue. This paper describes some of these approaches to geothermal resource risk quantification. Merit Measures for Resource Risk Many possible merit measures can be devised for geothermal resource risk; we have found the following to be practically most useful: a) Potential Resource Base (MW): This measure can vary widely from project to project; the larger the resource base, the larger is the development potential and higher the economy of scale. b) Drilling Success Rate (%): This measure is usually presented as the percentage of drilled wells that are successful. However, there is no unique threshold of well success nor does drilling success necessarily guaranty the economic attractiveness of a well. We believe the best merit measure for drilling success is the average cost of drilling per MW capacity achieved in a drilling program, and we prefer to use this. c) Unit Capital Cost ($/kw): This is defined as the capital cost per MW of installed power capacity, which consists of (a) drilling, well testing and other resource supply costs, plus (b) the power plant and other surface facilities costs. d) Levelized Power Cost ( /kwhour): We define this as the initial capital investment plus the cumulative present value of future costs discounted by the cost-inflation rate, divided by the cumulative power generation over the project life (Sanyal, 2005). This measure is a function of the inflation and interest rates, rather than a function of an arbitrary discount rate chosen to cover all project risks. e) Discounted Profit-to-Investment Ratio: This is defined as the ratio of the cumulative present value of future net 125

2 eturn (%) nal Rate of Re Inter revenues to the initial capital investment. An alternative to this measure is the overall rate of return (%) from a project, both being dependent on the discount rate chosen for cash-flow analysis. f) Internal Rate of Return (%): This measure is defined as the discount rate at which the cumulative present value of net future income becomes zero; it is independent of the discount rate chosen for cash-flow analysis. Capacity per Well (MW) Reserves (MW) Drilling Success Rate (%) Drilling Cost per Well (million$) Annual Harmonic Decline Rate (%) % 80% 60% 40% 20% 0% 20% 40% 60% 80% 100% Change from Base Case (%) Figure 1. Sensitivity of IRR to changes in resource risk parameters. Figure 2. Example of Monte Carlo simulation of reserves. 126 Resource Risk Quantification Approaches We use one or more of the following four approaches to quantifying resource risk utilizing any of the above merit measures: (a) sensitivity studies, (b) probabilistic assessment, (c) certainty-equivalent mapping (Au et al, 1972), and (d) design of experiments. The last of the above approaches will not be covered here; it is beyond the scope of this paper, being too involved for routine application in geothermal projects. Figure 1 is an example of a sensitivity study of the internal rate of return (IRR) of a geothermal project. This figure shows the percent change in IRR as a function of the percent changes from the base-case values of each of five key resource variables considered (reserves, MW capacity per well, drilling success rate, drilling cost per well, and annual rate of decline in well productivity). In this figure, the higher the slope of the curve representing the change in a resource variable, the more sensitive is the IRR is to that variable. In this example, the IRR is most sensitive to reserves, followed by capacity per well and drilling cost per well, in the decreasing order of sensitivity; the IRR is relatively insensitive to drilling success rate and annual harmonic decline rate in well productivity (Sanyal, 2005). Similar sensitivity studies can be conducted for the other merit measures to gain a quantitative understanding of the resource risk. Figure 2 shows the computed histogram and cumulative probability plots of the reserves estimated for a field using probabilistic simulation (Monte Carlo sampling) based on estimates of five fundamental resource variables: reservoir area, reservoir thickness, resource temperature, rock porosity and thermal energy recovery factor (Sanyal et al, 2004). Figure 2 presents the various statistical attributes (such as, mean, standard deviation, most-likely, P90, etc.) of the probability distribution of the resource estimate. This type of probabilistic quantification of risk is common for reserve estimation. The overall resource risk of a geothermal project can be quantified in a probabilistic way by defining the uncertainty profiles of one or more of the merit measures. In addition to utilizing the four fundamental resource variables (reserves, MW capacity per well, drilling success rate, drilling cost per well, and decline rate of well productivity), the estimation of three of the merit measures (levelized power cost, discounted profit-to-investment ratio and internal rate of return) also requires several variables that are not directly resource-related: power price ( /kwh), plant capacity factor (%), project life (year), injection well requirement (as fraction of the number of production wells), inflation rate (%), discount rate (%), royalty rate (%) on gross income, and tax rate (%) on net income. Figure 3 shows a schematic flow diagram of this quantification scheme. Figure 4 is an example of a certainty equivalent map of the reserves for a geothermal project at a 90% confidence level. This figure is a plot of the standard deviation versus mean of the MW reserves computed by Monte Carlo simulation from the fundamental resource variables (shown in the top-most row in Figure 3). The dots in Figure 4 represent

3 Figure 3. Quantification of the overall resource risk. ation (MW) ndard Devia Sta R = 136 MW R = 50 MW R = 118 MW R = 100 MW Pre Exploration Phase (Mean = 350 MW, Std.Dev = MW) Exploration Phase (Mean = 228 MW, Std.Dev = 99 MW) Confirmation Drilling Phase (Mean = 200 MW, Std.Dev = 50 MW) Development Phase (Mean = 150 MW, Std.Dev = 25 MW) Mean (MW) Figure 4. Certainty-equivalent map of resource base (90% confidence level). Table 1. Certainty-Equivalent Analysis of Reserves for a Geothermal Project at a 90% Confidence Level. Project Phase Mean (MW) Standard Deviation (MW) Certainty- Equivalent MW Pre-Exploration Exploration Confirmation Drilling Development the status of reserve estimation at the end of the various phases of a geothermal project, as summarized in Table The parallel lines through the various points in Figure 4 represent equal-risk lines drawn for a 90% confidence level. In this plot, the intersection point of an equal-risk line with the zero standard deviation axis represents the certainty-equivalent value of the estimated reserves at a 90% confidence level, assuming a normal probability distribution. If the required confidence level is different from 90%, the slope of the equal-risk lines will be different and can be computed. If the distribution of a merit measure is other than normal, the appropriate slope for the equalrisk lines can be estimated from probability theory. Table 1 lists the certainty-equivalent reserves (at 90% confidence level) at the various phases of the project. This table shows that in the pre-exploration phase, the certaintyequivalent reserves value (50 MW) was much smaller than the mean reserves (350 MW) because of the large uncertainty reflected in the relatively large standard deviation value (237.5 MW). With exploration, the mean came down (from 350 to 228 MW) but so did the standard deviation (from to 99 MW), and consequently the certainty-equivalent reserves in the exploration phase increased to 100 MW as compared to 50 MW in the pre-exploration phase. After confirmation drilling, the mean reserves as well as the standard deviation decreased, the certainty-equivalent reserves increasing to 136 MW at the end of the confirmation drilling phase. The certainty-equivalent reserves may not necessarily continue to increase through the successive phases of a project because exploration, drilling and well testing may uncover certain negative facts about the resource. In Figure 4, the standard deviation in the development phase (25 MW) is lower than in all earlier phases but the certainty-equivalent reserves (118 MW) are also lower than in the confirmationdrilling phase. Thus, certainty-equivalent mapping can be a practical tool in tracking resource risk as a project evolves through its phases. One important utility of certainty-equivalent mapping is that it allows a risk-averse investor to assess the risk-adjusted potential of a project while allowing the project promoter to get credit for the potential up-side in the project notwithstanding the high standard deviation. For example, in the pre-exploration phase, the project promoter may legitimately claim in this case a potential for up to 350 MW, while the investor may consider it to be a 50 MW project (the certainty-equivalent reserves) with a 90% level of confidence for investing purposes; yet both perceptions represent exactly the same reality. The Learning-Curve Effect on Resource Risk One important aspect of resource risk quantification is proper consideration of the learning-curve effect, which tends to reduce the risk. We will illustrate the learning-curve effect by considering the case history of the Kamojang geothermal field in Indonesia, which has a 25-year production history (Sanyal et al, 2000). Figure 5 presents the average drilling success rate at the Kamojang field, defining a successful well as one with a capacity of at least 3 MW, versus the cumulative number of wells drilled in the field. Figure 5 shows a rapidly increasing average drilling success rate with the cumulative number of wells drilled until the drilling success rate reached a relatively steady level of about 70%; this is an example

4 of the learning-curve effect. The 70% steady level of average drilling success, from a cumulative well count of about 40 to 80 is a consistent trend, and as such, statistically reliable. The issue of the learning-curve effect on the average power capacity per well is considered next. Figure 6 is a plot of the cumulative average MW capacity per successful well and the cumulative average MW capacity of all wells (successful or not) as a function of the cumulative number of wells drilled at Kamojang. The cumulative average capacity of all wells drilled reached a plateau, due to the learning-curve effect, after a well count of about 23. However, the cumulative average capacity of the successful wells continued to decrease slowly, due to the impact of reservoir pressure decline due to continuous production from the field (Sanyal et al, 2000). Even though Figure 6 does not show a pronounced plateau (reflecting the learning-curve effect) for the successful wells, it should be noted that at any cumulative well count, the ratio of the average MW capacity of all wells to that of the successful wells remains approximately constant at 0.70, showing a consistency between the data in Figures 5 and 6. This uccess Rate (% %) age Drilling Su Avera Number of Wells Drilled Figure 5. Number of wells drilled vs. average drilling success rate, Kamojang Field. l (MW) pacity per Wel Cap Successful Wells All Wells Number of Wells Drilled Figure 6. Number of wells drilled vs. average MW per well, Kamojang Field, Indonesia. 128 consistency also implies that as the average capacity of the existing wells has declined slowly with time, the average capacity of the new wells has increased slowly with time due to the learning curve effect. The Kamojang case history shows the learning-curve effect on drilling success rate in the development and operation phases of a geothermal project. However, in practice, the learning-curve effect on resource risk can be even more important in the confirmation-drilling phase of a geothermal project compared to the development and operation phases; this is illustrated below. Learning-Curve Effect in the Confirmation-Drilling Phase Let us consider a drilling program consisting of 5 discovery/ confirmation wells, which is typical in the industry and is usually funded by equity investors before construction financing can be secured. Since construction financing depends on the outcome of confirmation drilling, any benefit from the learning-curve effect in this phase becomes highly desirable. If all 5 wells have an even chance of being successful, the cumulative probability of drilling a certain number of successful wells can be estimated from probability theory. However, such computation overlooks the fact that as each confirmation well is drilled and tested, it is likely that the database and insight about the resource would improve. This introduces a positive learning-curve effect which, in turn, should improve the chance of success for the next well; for example, from 50% chance of success for the first well to perhaps 55% chance for the second well, 60% chance for the third well, 65% chance for the fourth well, and so on. Such learning-curve effect, of course, would not materialize if a well being drilled fails to take advantage of any incremental insight gained or data gathered from wells drilled before. For example, drilling all five wells simultaneously using five drilling rigs would preclude this learning-curve effect. Let us now consider the impact of the learning-curve effect on the success of this five-well confirmation drilling program with the increasingly enhanced chances of success, as assumed above, for the successive wells. Figure 7 graphically presents the possible outcomes, 16 in all, of a four-well drilling program assuming the learning-curve effect described earlier. From this figure, the cumulative probability levels for a four-well program can be estimated. For a five-well drilling program, there are 32 possible outcomes, which would be too cumbersome to present graphically as shown for the four-well program with only 16 outcomes; however, cumulative probabilities can be estimated as shown in Figure 8. Figure 8 compares the computed cumulative probability of drilling various numbers of successful wells in a five-well drilling program with or without the learning-curve effect. This figure illustrates how the learning-curve effect can improve the probability of success in the confirmation-drilling phase. For example, Figure 8 indicates that for a five-well drilling program, the cumulative probability of getting at least 2 successful wells is 81.3% if there is no learning-curve effect but increases to 91.9% with the benefit from the learning-curve effect. Likewise, the learning-curve effect increases the cumu-

5 Well 1 (50% chance) Well 2 (55% chance) þ = 50% þ = 50% Successful Path Unsuccessful Path Well 3 (60% chance) þ = 27.5% þ = 22.5% þ = 27.5% þ = 22.5% Well 4 (65% chance) þ = 16.5% þ = 11.0% þ = 13.5% þ = 9.0% þ = 16.5% þ =11.0% þ = 13.5% þ = 9.0% þ = 10.73% þ = 5.78% þ = 7.15% þ = 3.85% þ = 8.78% þ = 4.73% þ = 5.85% þ = 3.15% þ = 10.73% þ = 5.78% þ = 7.15% þ = 3.85% þ = 8.78% þ = 4.73% þ = 5.85% þ = 3.15% All 4 wells outcome 1st, 2nd, and 3rd wells successful 1st, 2nd, and 4th wells successful 1st and 2nd wells successful 1st, 3rd, and 4th wells successful 1st and 3rd wells successful 1st and 4th wells successful 1st well successful 2nd, 3rd, and 4th wells successful 2nd and 3rd wells successful 2nd and 4th wells successful 2nd well successful 3rd and 4th wells successful 3rd well successful 4th well successful All 4 wells unsuccessful Figure 7. Possible outcomes of a four-well program with positive learning-curve effect. lative Probability (%) Cumul Without Learning Curve Effect (50% chance for each well) With Learning Curve Effect (50% chance for well 1 to 70% chance for well 5) Minimum Number of Successful Wells Figure 8. The effect of learning-curve on a five-well exploration/confirmation-drilling program. Figure 9. The Portfolio Effect. lative probability of getting at least 3 successful wells from 50% to 68.4%, and the cumulative probability of getting at least 4 successful wells from at least 18.7% to 33.4%. In a five-well drilling program, 2 to 4 successful wells are typically expected as a pre-condition for financing, while the expectation of 5 successful wells would be optimistic. Figure 8 shows that the learning curve effect has the most positive impact over the 2 to 4 successful well range. The Portfolio Effect One practical approach to reducing resource risk for a developer would be to have a portfolio of projects in multiple locations. From probability theory, it can be shown that the standard deviation of any merit measure reflecting project risk for a multi-project portfolio would be a fraction of what it would be for a single project, the fraction being approximately 1/n 1/2 for a portfolio of n similar projects. This fact is shown graphically in Figure 9; it shows that the standard deviation for a four-project portfolio would be about half of that for a single project. Even a two-project portfolio reduces the standard deviation from 10 (for a single-project portfolio) to 7 (Figure 9). There are several other aspects of the portfolio effect that can reduce resource risk. For example, the risk that all projects would be unsuccessful drops rapidly with the number of projects in a portfolio. If there is a 10% chance that a project can fail, a single-project portfolio has 10% chance of failure while a five-project portfolio has a negligible chance (0.001%) of failure. Another positive impact of the portfolio effect on resource risk is seen in the development of multiple projects from a large inventory of available fields. Such a large inventory would generally have a log-normal distribution in resource base. It can be shown in such a case that the mean resource base in the portfolio as well as the largest project size would increase as the number of projects in the portfolio increases. Case History of a Low-Risk-Profile Project Figure 4 illustrates the evolution of the resource risk of a geothermal project as it passes through the various phases by considering the changes in a merit measure. The less the change in the certainty-equivalent value of a merit measure as the project progresses through the various phases, the lower is the project s risk profile. Let us consider the case history of the Kamojang project discussed before. Table 2 presents the status of the Kamojang project at the end of three distinct phases of this project: (Exploration Phase), (Development Phase) and (Operations and Expansion Phase); the table lists the known resource parameters at the end of each phase. Using the data from Table 2 and other information from the field, the levelized power cost for the project at various times in its history was estimated probabilistically (Figure 10). Figure 10 presents a certainty-equivalent map, for 90% confidence level, showing these estimated levelized power costs. This figure shows that the certainty- 129

6 ) Sanyal and Morrow Table 2. Evolution of resource risk in Kamojang Field, Indonesia Reservoir Area (km2) Number of Wells Drilled Average Drilling Success Rate (%) Cumulative Well Capacity (MW) Average Well Capacity (MW) Average Capacity of Successful Wells (MW) Average Drilling Rate (M/Day) Cost ( /kwh) St d. Dev. in Lev velized Power Kamojang Field (1988) Kamojang Field (2009) Kamojang Field (1996) Potential Reserve (MW) P Plant life (years) N 30 Initial capacity per well WI Initial number of production wells (including at least 1 stand-by well) NWI Minimum desired production capacity reserve R 0 Initial annual decline rate in well capacity DI Drilling cost per initial production well ($) CWI 3,000,000 4,000,000 3,329,583 Time when make-up well drilling is stopped (years) ITD 20 Capital cost ($/kw) C 3000 # Initial O&M cost CO Annual inflation rate XI 0.04 Annual discount rate D 0.15 Annual production (kwh) G 1,042,443,362 Availability factor 0.85 Drilling Success Rate (%) SUC Levelized Cost COSTL 5.98 Average levelized cost 6.07 ( /kwh) Standard deviation 0.07 Variance 0.00 Lower bound for 95% confidence interval 6.07 Upper bound for 95% confidence interval 6.07 Minimum 5.93 Maximum Conclusions Mean Levelized Power Cost ( /kwh) Figure 10. Certainty-equivalent map of levelized power cost of a low-riskprofile project. 1. Several practical merit measures for geothermal resource risk are available. 2. Geothermal resource risk can be quantified in either deterministic or probabilistic way, and by directly considering a resource risk element or indirectly through consideration of the cost consequence of the risk element. 3. Several approaches are available for risk quantification: sensitivity studies, probabilistic studies, certainty-equivalent mapping, etc. 4. We find the certainty-equivalent mapping to be the best overall tool for quantifying geothermal resource risk. 5. The learning-curve effect and the portfolio effect can have significant positive impact on resource risk. Acknowledgement The authors gratefully acknowledge the help received from Mr. Surya Darma, President of the Indonesian Geothermal Association (INAGA), in completing the database on the Kamojang project. References Table 3. Levelized power cost at Kamojang (1996). equivalent value of levelized power cost over the project life has changed from 5.81 /kwhour to 6.11 /kwhour, that is, by a mere 5% over a 21-year period, during which many wells have been drilled and the plant has been operated. Therefore, the Kamojang project illustrates the case of a low-resource-risk profile. The above example also shows another practical utility of the approach of certainty-equivalent mapping, which we find to be the best overall tool to quantify resource risk. Au, T., R.M. Shane and L.A. Hoel, Fundamentals of Systems Engineering, Probabilistic Models, pp Reading, MA: Addison-Wesley, Sanyal, S.K. (2005). Levelized Cost of Geothermal Power How Sensitive is it? Trans. Geothermal Resources Council, Vol. 29, pp Sanyal, S.K., A. Robertson-Tait, C.W. Klein, S.J. Butler, J.W. Lovekin, P.J. Brown, S. Sudarman and S. Sulaiman (2000). Assessment of Steam Supply for the Expansion of Generation Capacity from 140 to 200 MW, Kamojang Geothermal Field, West Java, Indonesia. Proceedings of the World Geothermal Congress, Beppu and Morioka, Japan, May-June, Sanyal, S.K., C.W. Klein, J.W. Lovekin and R.C. Henneberger (2004). National Assessment of U.S. Geothermal Resources A Perspective. Trans. Geothermal Resources Council, Vol. 28, pp