Using Fuzzy Logic to Identify Geothermal Resources and Quantify Exploration Risk through Play Fairway Analysis

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1 PROCEEDINGS, 41st Workshop on Geothermal Reservoir Engineering Stanford University, Stanford, California, February 22-24, 2016 SGP-TR-209 Using Fuzzy Logic to Identify Geothermal Resources and Quantify Exploration Risk through Play Fairway Analysis Yingqi Zhang 1, Drew Siler 1, Patrick Dobson 1, Colin Ferguson 2, Erika Gasperikova 1, James S. McClain 2, Peter Schiffman 2, Nicolas F. Spycher 1, Robert Zierenberg 2 1 Lawrence Berkeley National Laboratory, One Cyclotron Road, MS74-316C, Berkeley, CA University of California, Davis, One Shields Avenue, Davis, CA yqzhang@lbl.gov Keywords: Geothermal play fairway analysis (GPFA); fuzzy logic; risk ABSTRACT The objective of this work is to develop a methodology based on fuzzy logic to address the overarching theme of uncertainty quantification and reduction in identifying geothermal resources through Geothermal Play Fairway analysis. The study area includes regions from northeastern California, southern Oregon, and northwestern Nevada, bounded on the east by the Basin and Range extensional regime, and on the west by the Cascade (volcanic) Range. This is a region where geothermal resources are known to exist based on past exploration efforts, but their extent, risk and exploitability are poorly understood and understudied on both local and regional scales. Two main geothermal resource elements are investigated: permeability and heat. The available data used to explain these two elements are structural data (including fault length, age, stress, strain and seismicity) and heat source related measurements (including maximum heat flow data, maximum temperature data, maximum downhole temperature, smoothed heat flow, and geothermometry measurements). Fluid geochemistry data and some geophysical measurements (e.g., magnetotellurics data) are investigated, but not included in the assessment due to limited regional coverage. To apply fuzzy logic for identifying blind geothermal resources, first, a set of fuzzy numbers and rules are formed based on data histograms and expert opinion. Then for each grid block (the study region was discretized into grid blocks with a size of 2 2 km), a fuzzy logic rule is applied to combine different data types to arrive at a favorability map and the uncertainty associated with the map. The final map is able to identify known geothermal resources and new areas with potential. The proposed methodology is generic and can be applied to other areas. 1. INTRODUCTION Play Fairway Analysis (PFA) is a technique that has been used for oil and gas exploration to identify prospective resources for hydrocarbon extraction. The technique evaluates key elements required for the existence of such resources within a given geologic province. When it is used in geothermal exploration (e.g., Weathers et al., 2015), the key elements include: heat source, permeability, fluid to carry heat to surface, a reservoir unit, and cap rock. The objective of this study is to develop a method using play fairway concepts to identify geothermal resources. The method should be able to provide a probability map of geothermal resources as well as the uncertainty associated with such a map (i.e., to be used to quantify risk of failure). Our study area (Figure 1) includes regions from northeastern California, southern Oregon, and northwestern Nevada, bounded on the east by the Basin and Range extensional regime, and on the west by the Cascade (volcanic) Range. Two geothermal play type end-members, Medicine Lake (volcanic-hosted) and San Emidio (amagmatic extensional-hosted), are also included in our analysis. They are known geothermal systems that can be used to test our proposed method. While a variety of different geothermal play types have been identified by previous studies (e.g., Walker et al., 2005; Bogie et al., 2008, Erdlac et al., 2008; Moeck, 2014), two of the most prominent types of geothermal systems are volcanically-hosted systems, where volcanism and associated intrusions provide the necessary heat, and extensional systems, where the heat source is the deeper crustal or upper mantle rocks brought closer to the surface by tectonic extension. Our study region includes both types of geothermal systems, as well as transitional plays that may include the attributes of both. For a poorly explored or blind transitional system, conducting geothermal PFA (GPFA) based on purely volcanic or tectonic characteristics may miss or understate the resource. With this in mind, we develop GPFA approaches that exploit and combine the characteristics of both play types, without explicitly using any characteristics of both play types. The play fairway analysis process typically includes four steps: 1. Collect and compile available data and information for the area(s) to be evaluated; 2. Pre-process data (e.g., map available information onto the working grids; remove low quality data, normalize data); 3. Evaluate the probability of each key element to be present for the system considered; 4. Integrate all data to construct a final probability map with uncertainty range of the probability. In this paper we use the fuzzy logic approach for data integration to construct geothermal potential map. Fuzzy logic has been used to predict/estimate geological system properties in subsurface modeling. For example, Finol and Jing (2002) demonstrated how fuzzy rule- 1

2 based modeling can be used to predict permeability in sedimentary rocks based on well log responses; Zhang et al. (2010) developed a fuzzy rule-based model to predict connectivity of a fault system based on fault distribution; Kollias et al. (1999) showed how to map soil resources of a recent alluvial plain using fuzzy sets based on soil data. Reasons why fuzzy logic is a an appropriate technique for the GPFA include: 1. Fuzzy logic has the advantage of easily incorporating linguistic expert knowledge to identify geothermal resources or estimate properties; 2. There exist a variety of data types, but some types of data may be sparse. It is relatively easy to include all these data into resource evaluation using fuzzy logic; and 3. The result from fuzzy logic evaluation provides an uncertainty range, which can be used in the risk assessment of the evaluation. For this study, the fuzzy logic tool box from Matlab is used to perform such an evaluation. We first briefly discuss the data that are available for GPFA for the study region. Then we focus on the development of fuzzy logic approach on data integration and probability map construction, followed by results and conclusion. Figure 1: Study region (black rectangle) with two training sites Medicine Lake (green rectangle) and San Emidio (red rectangle). These are plotted on top of a relief map with estimates of dilation tendency of known faults, and known geothermal systems. The Oregon border is at 42 N, and the California border is just west of the eastern boundary of the Surprise Valley box (blue rectangle). 2. DATA COMPILATION AND PRE-PROCESSING The data collected for the region studied are summarized in the following categories: 1. Geological (structural) data; 2. temperature/heat data; 3. fluid chemistry data; and 4. geophysical data. The goal is to gain information on the key elements (i.e., permeability, heat source, fluid, reservoir unit and seal) by interpreting and integrating these data. For the convenience of evaluation, the study area is discretized into 2 km by 2 km grid blocks, which results in a total of 12,960 grid blocks. We found through multiple iterations of different grid sizes that 4 km 2 is the appropriate size to represent the extent of a typical western US geothermal reservoir, yet large enough to incorporate multiple data points in areas of sparse data. The above mentioned data are intended to be used as proxies to evaluate the geothermal potential for each grid. 2.1 Geological data Permeability in geothermal systems is commonly structurally controlled. Fault length, age, slip, and dilation tendency of faults were calculated and are used as proxies for favorability of fault permeability because: 1. We consider the likelihood of potential permeability conduits is higher with more faults present; 2. active tectonism is an important factor in generating and maintaining permeability pathways necessary for robust geothermal upflow (Bell and Ramelli, 2007, 2009; Faulds et al., 2012); and 3. critically stressed fault segments have a relatively high likelihood of acting as fluid flow conduits (Zoback and Townend, 2001; Ito and Zoback, 2000; Townend and Zoback, 2000; Barton et al., 1995, 1998; Morris et al., 1996; Sibson, 1994, 1996). The tendency of a fault segment to slip (slip tendency; T s ) (Morris et al., 1996) or to dilate (dilation tendency; T d ) (Ferrill et al., 1999) provides a quantitative indication of the resolved stresses on a certain fault segment, relative to another fault segment. If we assume that most faults are relatively near to a critically stressed state (a safe assumption in an area of active tectonism), slip tendency and dilation tendency serve as quantitative proxies for the stress state of the fault, and therefore serve as indicators of their likelihood to conduct fluids. 2

3 The second factor considered in geological data is the existance of favorable structural settings, which include horse-tailing fault terminations, fault intersections, and fault step overs. These features have been recognized to be the most common structural settings in the Great Basin and host the majority of known geothermal systems (Faulds et al., 2011, 2010, 2006; Hinz et al., 2011, 2010, 2008). Spatial correlations between high-temperature geothermal systems and elevated strain-rate (Faulds et al., 2012) suggest that active tectonism is an important factor in generating and maintaining permeability pathways necessary for robust geothermal upflow. As a result, we utilize measurements of active tectonism as proxies for permeability, including strain-rate and moment magnitude of earthquakes. To summarize, we have considered four geological factors related to permeability: fault favorability (which includes fault age, length, and slip/dilation tendency), structural setting type, strain rate, and magnitude of earthquakes. These factors are used to evaluate permeability favorability for each grid block. 2.2 Temperature/heat data In this category, we incorporate the following data: heat flow data, temperature gradient data, and temperature measurements. There are two types of heat flow data. The first type is the maximum heat flow at USGS wellbore locations. The measurements are relatively reliable, but there are only 74 measurements among all the 12,960 grid blocks. The second type of heat flow data is a smoothed heat flow map generated by the USGS (Williams and DeAngelo, 2011) through smoothing, interpolation, and extrapolation processes. The advantage of this map is that the smoothed heat flow is available for each grid block, but the high and low values are smeared out and the interpolated or extrapolated data are not as reliable as the ones directly taken from the wells. Temperature gradient data at some well locations provide similar information as heat flow. The measurements have the same problems as heat flow measurements at wells, i.e., the data are too sparse (only at 136 locations over the study area). A linear correlation is expected and found between the maximum heat flow and temperature gradient at the same locations. This relationship can be used to predict maximum heat flow at locations where temperature gradient data are available, but heat flow measurements are not. Direct temperature measurements with known maximum well depths are available at 194 locations. We assume that these measurements were taken at the bottom of the well. So a similar measure to geothermal gradient the temperature divided by well depth, is used in the evaluation of heat. 2.3 Fluid chemistry data Water chemistry data were collected and compiled, consisting of As/Cl, Na/K, Ca/Mg, SiO 2 /Cl, B/Cl, and SO 4 /Cl dissolved concentration ratios, excess 18 O (calculated as the shift in 18 O from the local meteoric line at the measured D value), and the logarithm of the partial pressure of dissolved CO 2 (pco 2 ). The various concentration ratios are selected on the basis of typical fluid chemistry trends observed in hydrothermal systems, e.g., decreasing Na/K ratios with increasing temperature driven by the reaction of Na- and K-feldspars. The first step is to calculate correlations between fluid chemistry and heat flow/temperature data, or correlation among these data. However, because the data are point measurements, the number of locations that have at least two types of measurement is very small. There is not enough statistical significance to make meaningful interpretation. For those areas where the sample size was adequate (mainly smoothed heat flow and one type of concentration ratios), no significant correlation is found. As a result of insufficient sample size, no reliable interpretation can be made. Therefore, these measured ratios are not used in the probability map construction. In addition, the Na/K, SiO 2 (quartz, conductive) and K/Mg geothermometers (Giggenbach, 1988; Fournier and Potter, 1982) were calculated. The sample size of Na/K geothermometer is 760, significantly larger than the other two (which are 44, and 47 respectively). We consider Na/K geothermometer value relatively reliable because it is not affected by dilution or evaporative concentration. As a result, these 760 geothermometer values are used in the heat evaluation. 2.4 Geophysical data Magnetotellurics (MT), a non-invasive geophysical method, can be used to indirectly detect and image resistivity anomalies associated with critical reservoir structural features, such as faults or fractures that might provide conduits for the flow of geothermal fluids, and lower permeability seals that may constrain the reservoir geometry. Resistivity is sensitive to the presence of fluids or magma, or clays, and in most cases it is also an excellent indicator of alteration mineralogy (e.g., Ussher et al., 2000; Cumming and Mackie, 2010). Combining and correlating these data with available data from other sources, e.g., surface geologic mapping, existing well logs, direct temperature measurements from wells and water chemistry, results in a more complete analysis and provides information in areas where other measurements may not be available. While a correlation is observed for resistivity and well temperatures (assumed to be taken at the maximum well depth) at Medicine Lake, MT data for the study region are sparse or not publically available. As a result, geophysical data are not used in the current GPFA. Figure 2 summarizes all the data used in the GPFA of the study region. Currently we only have data to infer permeability and heat favorabilities. Our focus is to develop the fuzzy logic data integration method and demonstrate the proposed method, creating not only a probability map for potential geothermal resources, but also providing an uncertainty range of the probabilities. We recognize a thorough and complete GPFA will require information on all essential elements mentioned previously. However, we can achieve our 3

4 goal by demonstrating our proposed method with only permeability and heat. The method would work the same way if additional data were available. Figure 2: Data types used in fuzzy logic analysis to evaluate probability map of potential geothermal resources. Orange color represents original data type. Grey colors are inferred quantity. Each dashed-line box contains information evaluated at the same time. 3. USING FUZZY LOGIC FOR DATA INTEGRATION TO CONSTRUCT PROBABILITY MAP The primary purpose of fuzzy logic is to formalize reasoning in natural language. A simple fuzzy if-then rule assumes the canonical form. For example, one of the many fuzzy rules to evaluate fault favorability for permeability can be formulated as: If a fault at a location is LONG, and YOUNG, and the fault stress is HIGH, then the fault is FAVORABLE to permeability. To be able to apply this rule, it is necessary to define fuzzy numbers for LONG or YOUNG fault, HIGH stress, and FAVORABLE to permeability. In fuzzy logic, they are defined using membership functions. These functions are discussed below for both permeability and heat attributes. 3.1 Evaluation of Permeability Figure 3 shows how membership functions are defined for each fuzzy number representing variable fault length. X-axis is the logarithm of a fault length. Y-axis defines the membership. A short fault is defined for the logarithm (base10) of the fault length log 10 (L) between 0 and 3.5, the membership for a fault with log 10 (L) between 0 and 3 to be short is 1, and a fault with log 10 (L) 3.5 to be short is 0; medium defined for 3 log 10 (L) 4; and long for log 10 (L) 4. Based on these definitions, a degree of membership of each grid block in the fuzzy set will be calculated. For example, if a grid block with faults has log 10 (L)=3.25, the membership that it is short is 0.5; the membership that it is medium is 0.5; and the membership that it is long is 0. For each type of data, the membership functions are defined based on the histograms of all the 12,960 data points. Figure 3. Membership functions for fuzzy numbers representing variable fault length. Similarly, membership functions are defined for variables fault age, and fault stress (use average of slip and dilation tendency). The next step is to define a set of fuzzy rules to infer favorability of a fault to permeability. Ideally, the rules should be derived from learning sites. Because the learning sites, in our case, Medicine Lake and San Emidio, have limited and sparse data, the rules in this project are derived based on expert-knowledge. The data from the two learning sites will be used to verify the results. 4

5 Figure 4. Screen shot of some rules to infer fault favorability to permeability. A total of 33 rules are defined to infer fault favorability to permeability. Figure 4 is a screen shot of some of those rules. For each grid block to be evaluated, usually multiple rules are applied. Rules are then combined using the standard inference method mamdani, provided by Matlab, as shown in Figure 5. The output is an aggregated membership function which, in the end, is usually defuzzified by some averaging processes (e.g., using the centroid ). In addition to this centroid F m (i.e., average favorability), the lower (F l ) and upper (F u ) bound of the membership can be used to define the (uncertainty) range of the fault favorability. Because fault favorability is not the final output of interest, we use the F l +( F m - F l )/3 as the lower bound and F u -( F u F m )/3 as the upper bound to enter the next step of evaluation. A similar approach is used for the next step of evaluation, which includes setting type, seismicity, strain rate and fault favorability to create a permeability map. There are total of 41 rules for this evaluation. Fault favorability is represented by three numbers: the lower bound leads to a lower bound of the permeability map, the average leads to the mean permeability map and the upper bound leads to the upper bound of the permeability map. Figure 5. Fuzzy inference system for fault favorability to permeability. 3.2 Evaluation of Heat Table 1 lists the total number of available data (including temperature inferred using geothermometer measurements) used for heat evaluation. Property Smoothed heat flow Max. temperature divided by depth Max. heat flow Max. temperature gradient Na/K geothermometry Number Table 1. Data used to evaluate heat 5

6 The evaluation of heat is a little different than the evaluation of permeability for two reasons: 1. Only smoothed heat flow is available for all the grid blocks; all other types of data have much less spatial coverage; and 2. The quality of each type of data is clearly different (e.g., the smoothed heat flow is not the best for heat evaluation as the peak heat flow does not stand out due to the smoothing process, as the USGS heat flow map for the western United States was generated with a cap on the maximum heat flow value of 120 mw/m 2 to minimize the influence of anomalously high heat flow associated with hydrothermal systems (Williams and DeAngelo, 2011)). As a result, preferences are made for different types of data, with maximum heat flow/temperature gradient (the linear functional form obtained from Figure 6 is used to predict maximum heat flow at locations where it is not available but maximum temperature gradient is) most preferred. The membership function of each variable is defined based on the histogram data, which provide the range of the data. The first step is to check if maximum heat flow and temperature gradient are available for a location. If the answer is yes, then the heat is evaluated based on the histogram data (which provide the range of the data), the score on heat is assigned with a small uncertainty range. If the answer is no, then the heat is evaluated based on smoothed heat flow, maximum temperature divided by well depth, and geothermometry using fuzzy logic. The corresponding evaluation is assigned a larger uncertainty range. Maximum temperature divided by well depth and geothermometry are never used for evaluation by themselves, but are always combined with smoothed heat flow. The locations with only smoothed heat flow for heat evaluation are assigned the largest uncertainty range. Again, the membership function for each type of data is defined based on the histogram of that type of data. These fuzzy rules include rules for unavailable data (e.g., only smoothed heat flow exists for all locations, so it is the only available data for many locations). Figure 6. A plot of maximum heat flow vs. maximum temperature gradient shows a linear relationship between the two. 3.3 Construction of Favorability Map For each grid block, now there is a favorability score with upper and lower bounds for both permeability and heat. To construct the overall favorability map, we have defined five fuzzy numbers for permeability (see Figure 7a), similar five fuzzy numbers for heat and nine fuzzy numbers for the final favorability (see Figure 7b). Twenty-six rules shown in Figure 8 are used to evaluate the overall geothermal potential for each grid block in the study area. Figure 7. Fuzzy numbers used to define a. permeability favorability and b. overall favorability 6

7 Figure 8. Fuzzy rules used to infer overall favorability from permeability and heat evaluation. 4. RESULTS The mean favorability of permeability and heat maps are shown in Figure 9. The large blue area in heat map reflects a lack of thermal data. These maps show that Medicine Lake does not have high favorability for permeability (as defined by our fuzzy logic rules), while San Emidio does, reflecting that the latter is an extensionally-hosted site, while Medicine Lake is a volcanic-hosted system. However, Medicine Lake has highly favorable values for heat source, while San Emidio has a high heat rating, but spanning a much smaller area because of limited data coverage. Note, we did not derive our fuzzy rules based on these two learning sites, so the results at these two sites can be used to validate our proposed method. In addition to the mean favorability map, both upper and lower bound maps were generated (not shown here), providing the basis for risk assessment for these resources. (a) (b) Figure 9. Computed mean favorability rank (between 0 and 1) for (a) permeability and (b) heat using fuzzy logic the higher the rank, the more favorable it is to the presence of geothermal resources. Figure 10a shows the overall potential geothermal resource (mean). Medicine Lake and San Emidio clearly stand out. In addition, the Lakeview area in Oregon also appears as a prospective target, as it is known KGRA and the site of a new district heating project. These identified red spots confirm the validity of the used methodology: even though fuzzy rules are only generated from expert knowledge (i.e., no learning site data are used), the final evaluation is able to identify existing geothermal resources. We also show in Figure 10b the upper bound of the favorability map, as the upper bound can identify the risk-high benefit regions. These are the regions where more data should be collected to further determine if more focused exploration activities should be carried out. 5. CONCLUSION In this study we use a fuzzy logic approach to integrate various types of data for identification of geothermal resources. The fuzzy logic approach has the advantage of formalized reasoning in natural language, which helps to apply expert opinion into modeling practice. Due to the large area studied, we have a range of locations; some hardly having any data, while other locations having multiple, repetitive information. Fuzzy logic can easily handle both of these situations and provide an uncertainty range based on how much/what information is available. For the study region, we identified three prospective target areas that have been proven to have geothermal potential, which provides confidence in the proposed method. 7

8 Even though we have not considered all the attributes needed for geothermal resources in this analysis, using permeability and heat attributes only is sufficient to demonstrate our proposed method. When available, additional attribute data can be easily included in the evaluation. (a) (b) Figure 10. Computed overall favorability rank: (a) mean value and (b) the upper bound maps. Circled regions represent areas recommended for future study. ACKNOWLEDGMENTS We wish to thank Colin Williams and Jake DeAngelo (USGS) for sharing their heat flow and well temperature data for our study area. We also thank Ian Warren (US Geothermal) for providing us with detailed information on the San Emidio geothermal field, and Joe Moore (U. Utah) for sharing copies of well logs from San Emidio. This work was supported by U.S. Department of Energy Award EE to UC Davis and funding by the Assistant Secretary for Energy Efficiency and Renewable Energy, Geothermal Technologies Office, of the U.S. Department of Energy under the U.S. Department of Energy Contract No. DE-AC02-05CH11231 with Lawrence Berkeley National Laboratory REFERENCES Bardossy, A., and Duckstein, L.: Fuzzy Rule-Based Modeling with Applications to Geophysical, Biological and Engineering Systems, CRC Press, Boca Raton, FL (1995), Barton, C.A., Hickman, S.H., Morin, R., Zoback, M.D., Benoit, D.: Reservoir-scale fracture permeability in the Dixie Valley, Nevada, geothermal field. Proceedings, Soc. Pet. Eng. Annu. Meet., (1998) doi: /47371-ms Barton, C.A., Zoback, M.D., Moos, D.: Fluid flow along potentially active faults in crystalline rock, Geology, 23, (1995) Bell, J.W., and Ramelli, A.R.: Active Faults and Neotectonics at Geothermal Sites in the Western Basin and Range: Preliminary Results. Geothermal Resources Council Transactions, 31, (2007)

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