Lithology identification of aquifers from geophysical well logs and fuzzy logic analysis: Shui-Lin Area, Taiwan $

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1 Computers & Geosciences 31 (2005) Lithology identification of aquifers from geophysical well logs and fuzzy logic analysis: Shui-Lin Area, Taiwan $ Bieng-Zih Hsieh, Charles Lewis, Zsay-Shing Lin Department of Resources Engineering, National Cheng Kung University, Tainan, Taiwan Received 7 July 2003; received in revised form 7 July 2004; accepted 16 July 2004 Abstract The purpose of this study is to construct afuzzy lithology system from well logs to identify formation lithology of a groundwater aquifer system in order to better apply conventional well logging interpretation in hydro-geologic studies because well log responses of aquifers are sometimes different from those of conventional oil and gas reservoirs. The input variables for this system are the gamma-ray log reading, the separation between the spherically focused resistivity and the deep very-enhanced resistivity curves, and the borehole compensated sonic log reading. The output variable is groundwater formation lithology. All linguistic variables are based on five linguistic terms with a trapezoidal membership function. In this study, 50 data sets are clustered into 40 training sets and 10 testing sets for constructing the fuzzy lithology system and validating the ability of system prediction, respectively. The rule-based database containing 12 fuzzy lithology rules is developed from the training data sets, and the rule strength is weighted. A Madani inference system and the bisector of area defuzzification method are used for fuzzy inference and defuzzification. The success of training performance and the prediction ability were both 90%, with the calculated correlation of training and testing equal to and 0.928, respectively. Well logs and core data from a clastic aquifer (depths m) in the Shui-Lin area of west-central Taiwan are used for testing the system s construction. Comparison of results from core analysis, well logging and the fuzzy lithology system indicates that even though the well logging method can easily define a permeable sand formation, distinguishing between silts and sands and determining grain size variation in sands is more subjective. These shortcomings can be improved by a fuzzy lithology system that is able to yield more objective decisions than some conventional methods of log interpretation. r 2004 Elsevier Ltd. All rights reserved. Keywords: Groundwater; Aquifer characterization; Hydrogeology; Artificial intelligence; Soft computing 1. Introduction $ Code available from server at Corresponding author. Tel.: ; fax: addresses: wink@ms31.url.com.tw (B.Z. Hsieh), zsaylin@mail.ncku.edu.tw (Z.S. Lin). Fuzzy logic analysis of well logs has been recently applied extensively in many reservoir characterization studies. For example, Fung et al. (1997) applied a selfgenerating fuzzy rule extraction and inference system to the prediction of petrophysical properties from well log data, whereas Huang et al. (1999) presented auseful fuzzy interpolator for permeability prediction based on /$ - see front matter r 2004 Elsevier Ltd. All rights reserved. doi: /j.cageo

2 264 B.Z. Hsieh et al. / Computers & Geosciences 31 (2005) well logs from the North West Shelf in Australia. Fuzzy logic has also been used to determine hydrocarbon formation lithofacies and permeability from well log data in the southern North Sea (Cuddy, 2000). Cuddy s results gave near-perfect differentiation among aeolian, fluvial, and sabkha rock types (the major lithofacies in several North Sea fields) from basic logs such as gammaray (GR) and porosity logs. The techniques of fuzzy logic analysis from well logs can be applied to both consolidated and unconsolidated sediments, as well as for water applications in oil exploration. Although conventional geophysical well logging is an ideal method for hydro-geologic studies involving aquifer characteristics, such as porosity and hydraulic conductivity (Temples and Waddell, 1996; Lin et al., 1997), the identification of aquifer lithology from well log data depends upon the ability to distinguish between soils/rocks with grain sizes varying from clay to gravel, and this method is still largely subjective in the absence of core data. Well logging also provides in situ and continuous data, as well as yielding a number of economic benefits by saving the cost and time of core analyses. However, well logging is limited because lithology identification is still a subjective task that depends largely on the experience of the log analyst. Identification of hydrocarbon formation lithology from geophysical logs commonly employs lithology crossplots (such as M N lithology plot which requires asonic log, density log, and neutron log) or the combination gamma-ray neutron-density log method (Asquith and Gibson, 1982). However, consideration must be given to the idea that groundwater aquifers can be contaminated by the radioactive sources required for these two types of logs, and the large hydraulic conductivities might create an adverse environment for decentralized neutron and density logs (Peng, pers. comm., 2003). Furthermore, the lithologies involved in water wells versus oil/gas wells might require different log suites. Identification of groundwater (shallow aquifer) formation lithology from well log data largely depends on expert experience and rather subjective rules, such as, IF the natural GR reading is high and the separation in readings between shallow formation resistivity and deep formation resistivity is small, then the formation lithology is probably shale (Chapellier, 1992; Hsieh, 1997). Moreover, groundwater aquifer systems involving rocks with grain sizes ranging from clay to sand are often characterized by well logging methods as simply: sands (including fine-, medium-, or coarse-grained sands: the major components of an aquifer) and shales (including silts, clays, and muds : the major components of an aquitard). This type of analysis from well logging is simple and subjective. One way to reduce this subjectivity is with the fuzzy logic technique, atype of artificial intelligence (AI) technology that has been successfully used to determine hydrocarbon sediment lithology (Cuddy, 2000). Similar to conventional computerized well log analyses, fuzzy logic allows all pertinent log data, core analyses, mud analyses, etc. to be examined simultaneously by the interpreter. Although the fuzzy logic method uses the same data as conventional log analysis, it is unlike conventional analyses which still demands qualitative determination of lithology. Instead, fuzzy logic adopts a set of rules insuring objectivity in determination of soil/rock type whilst incorporating the expertise of the interpreter. The purpose of this study is to construct afuzzy lithology identification system based on the GR log, the resistivity logs, and the sonic log from the Shui-Lin area of Taiwan to identify formation lithology of a groundwater aquifer. The fuzzy logic lithology identification system can provide a more objective approach for log analysts in determining lithology in the gray areas (areas involving clastic rocks with grain sizes between sand and shale) of the system of interest. 2. Basic Theory 2.1. Conventional Well Log Analysis The hydro-physical logs used in this study are: (a) the GR, (b) borehole compensated sonic (BHC) with sonic porosity (SPHI) curve, (c) spontaneous potential (SP), and (d) phasor induction (PI). The PI includes four curves: medium very-enhanced resistivity (IMER), deep very-enhanced resistivity (IDER), spherically focused resistivity (SFLU), and apparent formation water resistivity (Rwa). The lithologic results of core analysis were also used in this study. This study limits the following explanation of conventional well log analysis basic theory to clastic sedimentary rocks, focusing on shales and sandstones and the different responses of logging tools to salt water versus fresh water zones. The following describes the basics of the log types used in this study to acquaint the general reader Gamma-ray (GR) log The GR log is designed to measure the natural radioactivity of soils and rocks, and is particularly useful in distinguishing between shales and sandstones and in determining depositional environments. Shales usually exhibit high GR readings if they contain sufficient quantities of accessory minerals containing isotopes like potassium ( 40 K), uranium ( 238 U) or thorium ( 232 Th). On the other hand, sands normally exhibit low GR responses (Fig. 1).

3 B.Z. Hsieh et al. / Computers & Geosciences 31 (2005) Fig. 1. Lithology determination from gamma-ray and resistivity logs. Table 1 Average interval transit time and velocity in rocks (after Sheriff and Geldart (1995); Chapellier (1992); Dewan (1983); Asquith and Gibson (1982)) Lithology Transit time, Dt (ms/ft) Velocity of matrix (ft/s) Velocity of matrix (m/s) Clays , Shale , Sandstone ,000 19, Limestone ,000 23, Dolomite ,000 26, Borehole compensated sonic (BHC) log with porosity curve (SPHI) Because of the overlap in velocities between sandstones and shales (Table 1), the primary function of a sonic log is seldom determination of lithology; however, it can sometimes provide useful information regarding rock type and porosity, particularly if this log is used in conjunction with other logs. For clean sandstones saturated with oil, salt water or fresh water, the sonic log may give similar responses, but gas usually has a more pronounced effect on this log. The bulk compressional wave velocity in rocks is also heavily dependent upon porosity, that decreases the velocity, and the primary wave velocity may depend upon degree of consolidation or packing as well. Generally, the velocity of acoustic waves is slower in clays than in sandstones (Table 1) Spontaneous potential (SP) log The secondary potential or SP log requires a conductive drilling mud for best results. According to Asquith and Gibson (1982), the magnitude of SP deflection depends upon the difference in resistivity between the mud filtrate and formation water, and if these two fluids have the same resistivity, there is no deflection of the SP from the shale baseline. Clean sandstones containing oil, gas and salt water have negative deflections (with salt waterooilogas), whereas clean sandstones containing fresh water might have zero or even positive SP responses. If the formation water is fresher than the mud filtrate, the curve will show a positive deflection, with the amount of deflection proportional to the difference in salinity between the formation water and mud filtrate Phasor induction (PI) log with apparent formation water resistivity (Rwa) curve The most useful log in this study for distinguishing fresh wateraquifersfromsaltwaterreservoirsisthepilog.it consists of curves for shallow, medium and deep resistivities, along with a curve for apparent formation water resistivity of the uninvaded zone where the formation water is uncontaminated by mud filtrate. Although induction logs do not work well in highly conductive muds, they can be run in holes filled with air, oil, or freshwater muds. Aquifers tend to be more resistive than aquitards. For a well drilled with salt water based drilling mud, the resistivity of the invaded zone, that consists of rock, mud filtrate, formation water (either salt or fresh water), and possibly residual hydrocarbons, will generally be smaller than the resistivity of the uninvaded zone containing fresh water. For this situation, porous and permeable sandstones are characterized by a wide separation between the shallow (invaded zone) and deep

4 266 B.Z. Hsieh et al. / Computers & Geosciences 31 (2005) (uninvaded zone) resistivity curves. On the other hand, under the same conditions above, a shale would exhibit a small separation between the shallow resistivity curve and the deep resistivity curve (Fig. 1). If, however, the drilling mud is fresh water based, the separation between the spherically focused (shallow) resistivity curve and the deep resistivity curve will be considerably less (the invaded zone resistivity can be approximately equal to that of the uninvaded zone since both contain fresh water) than if the drilling fluid were salt water based. The separation between the two resistivity curves is therefore an important parameter in lithology determination involving a groundwater aquifer, provided the type of drilling mud is known Fuzzy lithology system Fuzzy set theory, amethod to distribute linguistic fuzzy information by mathematics, distributes a set by using amembership function, and extends the concepts of classical set theory. Fuzzy logic can be defined as: a logical system that generalizes classical two-valued logic for reasoning under uncertainty (Yen and Langari, 1999). Therefore, fuzzy logic theory eliminates the problem of two-valued logic reasoning in classical set theory (Klir and Yuan, 1995). The major procedures in a fuzzy lithology system developed in this study include (i) fuzzification, (ii) fuzzy if-then rules database, (iii) fuzzy inference system and (iv) defuzzification (Fig. 2). During fuzzification, well log data (such as the GR reading, the separation between resistivity curves (DR), and the interval transit time (Dt)) are transformed to linguistic input variables constructed by linguistic terms and a membership function. The fuzzy if-then rules database contains several lithology identification rules; the form of lithology identification rules is constructed by if A, B and C, then D where A, B, C, and D are fuzzy sets. Fuzzy approximate reasoning is then determined by a fuzzy inference system. A fuzzy lithology value is obtained by a defuzzification method, and finally the lithology of groundwater formation can be determined Fuzzification The fuzzy lithology system in this study contributes the linguistic variables from the original domain Well log reading Fuzzification Linguistic input variables Fuzzy if-then rules database Fuzzy inference system Fuzzy lithology value Fig. 2. Fuzzy lithology system. Defuzzification Lithology Fig. 3. Linguistic input variable model. Each linguistic input variable is constructed from five linguistic terms: VL (very low); L (low); M (medium); H (high); and VH (very high). variables. The linguistic input variables include GR, DR, and Dt, which are some of the most important basic parameters in lithology identification of groundwater formations. Every linguistic input variable involves five linguistic terms, such as very low (VL), low (L), medium (M), high (H), and very high (VH) as shown in the trapezoidal membership function (Fig. 3). The linguistic output variable is lithology, consisting of five linguistic terms: C (clay), Z (silt), FS (fine sand), MS (medium sand), and CS (coarse sand). The reference boundary of the output variable linguistic term is defined as an exponent. The grain size range is presented by an exponential function (of the form 2 n, where n is anegative integer) (Table 2). From the range of grain size, the exponent n for the upper and lower boundaries is adopted to define the reference boundary of linguistic terms. The membership function adopted for the linguistic output variable is a trapezoidal membership function (Fig. 4) Fuzzy if-then rules and rule-based database The rule-based database consists of several general lithology identification rules. The format of the lithology identification rule is If GR is A, and DR is B, and Dt is C, then lithology is D. Where GR, DR, a nd Dt are linguistic input variables; lithology is the linguistic output variable; A, B, C are linguistic terms of input variables (VL, L, M, H, or VH); and D are the linguistic terms of output variables (C, Z, FS, MS, or CS). The number of lithology identification rules depends on the training data. For example, if all combinations between every two input variables are considered, the rule-based database consists of a total 125 (=5 3 ) ifthen rules. Therefore, an appropriate reduced rulebased database must be incorporated into the system training step.

5 B.Z. Hsieh et al. / Computers & Geosciences 31 (2005) Table 2 Grain size range of matrix and reference boundary setting Linguistic term of output variable Grain size range of matrix (cm) Reference boundary of linguistic term CS (coarse sand) 2 0 4AGS * 42 1 [0, 1] MS (medium sand) 2 1 4AGS42 2 [ 1, 2] FS (fine sand) 2 2 4AGS42 4 [ 2, 4] Z (silt) 2 4 4AGS42 8 [ 4, 8] C (clay) 2 8 4AGS42 12** [ 8, 12] * AGS=Average grain size. ** 2 12 represents the value of zero. Fig. 4. Linguistic output variable lithology constructed from five linguistic terms: C (clay); Z (silt); FS (fine sand); MS (medium sand); and CS (coarse sand) Fuzzy inference system A Madani inference system was chosen for this study. Madani fuzzy inference uses a linguistic reasoning process that has been extensively applied to engineering studies (MATLAB, 2001). Because the output variable in this study is defined by fuzzy sets, the process of fuzzy reasoning belongs to a type of linguistic reasoning. Therefore, the Madani inference system is an appropriate method for this study Defuzzification The input for the defuzzification process is a fuzzy set and the output is a crisp set. The purpose is to derive a crisp value which can represent the result of fuzzy sets in linguistic output variables. The bisector of area method is introduced into the defuzzification process (MATLAB, 2001). This method bisects the aggregate output area and obtains the output crisp value from the center of the area. 3. Case study 3.1. Regional geology The Shui-Lin area, used for identifying lithologies of a groundwater aquifer system in this study, is located southwest of Yun-Lin, Taiwan (Fig. 5). The area is part of the south branch of the Chou-Shui River alluvial fan system, whose deposits consist of unconsolidated sand, silt, and clay from the Chou-Shui River and its tributaries. The upper section of the alluvial fan consists primarily of gravel deposits, whereas the lower section (Shui-Lin area) consists mainly of sand or clay. The interbedded shale aquitard and the sand aquifer were deposited because of alternating transgression and regression. All of the sedimentary formations in the investigation area are Pleistocene-Recent in age. In the Shui-Lin area, the shale materials (silt and clay) are aquitards, and the sands (FS, MS, and CS) are aquifers Data Collection The geophysical logs from SL-2 well used in this study (Fig. 6) include the GR log, api log consisting of three usual resistivity curves (the medium very-enhanced curve was not used in this study) plus an Rwa curve (not shown in Fig. 6), and a BHC log with SPHI curve (porosity curve not shown in Fig. 6). Lithologic types from core analyses from the SL-monitoring well include C, Z, FS, MS and CS. Both the geophysical logs from SL-2 well and the core analysis lithology from SL-monitoring well represent continuous data over the depth range from 100 to 198 m. Also, these two wells are located very close to each other (Fig. 5). The distance between the two wells is about 400 m. Because of their close proximity, it is assumed that their lithologies and depths are equivalent. 4. Procedure 4.1. Data digitization For the SL-2 wells, log curves were read every 2 m for the depth range from 100 to 198 m (drill depths with ground level equal to 7.1 m) and then converted to digital data sets. A total of 50 data sets were digitized (Table 3). Every log data set included the GR log, the SFLU and the IDER curves from the PI log, and the

6 268 B.Z. Hsieh et al. / Computers & Geosciences 31 (2005) Fig. 5. Study area and well locations. BHC log. The input parameters used in the fuzzy lithology system, GR and Dt, were directly taken from the digitized data of the GR log and the BHC log, respectively. The other input parameter, DR, is the value of the IDER (deep) curve reading minus the SFLU (shallow) curve reading. According to the core analysis from the Central Geological Survey of Taiwan, the lithology of the Shui- Lin area groundwater aquifer includes C, Z, FS, MS, and CS. In the fuzzy lithology system, the lithology type must be converted to a crisp set for system mathematical estimation. A code number from 1 to 5, ranging from coarse sand to clay, respectively, was assigned for each lithology (Table 4). Therefore, the input variables used in the fuzzy lithology system were GR, DR, a nd Dt. And the output variable used in the fuzzy lithology system was lithology. For the depth interval from 100 to 198 m, a total 50 datasets were collected and digitized (Table 3) Data cluster The 50 data sets were clustered into two parts: training data sets and test data sets. The training data sets were used to construct the fuzzy lithology system for Shui-Lin area by carefully adjusting the fuzzy sets of the fuzzy input variables, by reducing the fuzzy lithology rules, and by constructing the rule-based database. The test data sets were used to validate the ability of system prediction. Based on the 80/20 rule for the total of 50 data sets, the amount of the training data sets and the test data sets were 40 and 10, respectively. The following steps are necessary to extract the 10 test data sets: (1) arrange all sets in order of increasing depth (Table 3); (2) choose a random depth value among the 50 data sets (122 m was chosen at random in this study); (3) pick up the test data sets every 10 m spaced in the up direction from the chosen depth value (in this study, the testing data sets started from 122 m by random choice, the 112 and 102 m were extracted in the up direction) (Table 3); (4) pick up the test data sets every 10 m spaced in the down direction from the chosen depth value (in this study, based upon the 122 m depth selected by random choice, 132, 142, 152, 162, 172, 182, and 192 m were extracted in the down direction) (Table 3). Step (3) involving depths of 100, 102, 104, 106 and 108 m (chosen by random) can be ignored because no test data sets can be found in the up extracted direction. Step (4) can be ignored for depths of 190, 192, 194, 196 and 198 m (chosen by random) because no any test data sets can be found in the down extracted direction. By the way of test data set extraction, 10 test data sets, at depths of 102, 112, 122, 132, 142, 152, 162, 172, 182, and 192 m, were extracted. The reason for not extracting

7 B.Z. Hsieh et al. / Computers & Geosciences 31 (2005) Fig. 6. Geophysical logs from SL-2 well and core analysis from SL-monitoring well. all test data sets by random is to avoid the test data sets from becoming too concentrated in some depth intervals Fuzzy lithology system construction Based on the 40 training data sets, the linguistic input variables, including GR, DR, and Dt, can be constructed (Figs. 7 9). Every linguistic input variable is based on five linguistic terms: VL, L, M, H, and VH, respectively. The membership function adopted for linguistic input variable analysis is a trapezoidal membership function. The linguistic output variable is lithology, which is differentiated by five linguistic terms: C, Z, FS, MS and CS, respectively (Fig. 4). From the reference boundary defined (Table 2) and the trapezoidal membership function, an output fuzzy set, lithology, can be constructed (Fig. 4).

8 270 B.Z. Hsieh et al. / Computers & Geosciences 31 (2005) Table 3 Digitized well log data and resulting lithologies Depth GR * DR * Dt * Lithology ** Depth GR DR Dt Lithology * Digitized well logs: GR: Gamma-ray log reading, API; DR: Value of deep curve reading minus shallow curve reading, O-m; Dt: Borehole compensated sonic (BHC) log reading, ms/ft. ** Lithology abbreviation: 5 (clay); 4 (silt); 3(fine sand); 2 (medium sand); 1 (coarse sand). Table 4 Lithology code used in fuzzy lithology system Lithology (Shui-Lin area) Grain size range of matrix (cm) Correlated lithology code Coarse sand 2 0 4AGS Medium sand 2 1 4AGS Fine sand 2 2 4AGS Silt 2 4 4AGS Clay 2 8 4AGS42 12** 5 A reduced fuzzy lithology rule-based database was developed from the 40 training data sets. The rule-based database contains 12 fuzzy lithology rules (Table 5), which are all in the form of an if-then model. A rule weighting concept was introduced in this study for carefully adjusting the rule strength (MATLAB, 2001). Every rule can define arule weight, which is anumber between 0 and 1. A rule weight used in this study not only reflects the strength of the rule, but also expresses the relative importance between rules. Fuzzy reasoning for all rules in this study was based upon a Madani inference system. After the process of output aggregation, the bisector of area defuzzification method derives acrisp value which represents the result of aggregate output area. By using the reference boundaries for lithology types (Table 2), acrisp set derived from defuzzification can be converted to a specific lithology; thus, the lithology of the groundwater aquifer can be identified from the fuzzy lithology system. 5. Results By using the 40 training data sets, the specific fuzzy sets of input variables were constructed. A fuzzy lithology rule-based database, containing 12 fuzzy

9 B.Z. Hsieh et al. / Computers & Geosciences 31 (2005) Fig. 7. Linguistic input variable, GR, includes five linguistic terms (for definitions, see Fig. 3). Fig. 8. Linguistic input variable, DR, includes five linguistic terms (for definitions, see Fig. 3). Fig. 9. Linguistic input variable, Dt, includes five linguistic terms (for definitions, see Fig. 3). of the training data sets into the trained fuzzy lithology system. In this study, a total of 40 training data sets were used to check the performance of system training. The results of lithology from this fuzzy lithology system (named fuzzy lithology ) were compared with the results of lithology from core analysis (named true lithology ). In Fig. 10, the square marks (also connected by a line) represent the true lithology, the star marks represent the fuzzy lithology, the vertical axis shows the depth interval from 100 to 200 m, and the numbers from 1 to 5 on the horizontal axis represent the different lithologies from CS, MS, FS, Z, and C, respectively. Thirty-six training data sets were identified correctly from the total 40 training data sets (Fig. 10), for a success rate of 90%. In the performance validation of the system training, all of the sand types (CS, MS, and FS) were successfully identified (Fig. 10). Only four layers were not well trained. Even though the training performance was not perfect (success rate of 100%), but, in this study, the real performance of the system depended on the predictive ability as well; therefore, an appropriate training performance to avoid over-training (means the system had a perfect training result but poor predictive ability) was considered. On the other hand, achieving the best predictive ability of the system was the desired target Predictive ability of fuzzy lithology system (test results) Ten non-trained test data sets were introduced into the fuzzy lithology system for validating the predictive ability of the system. Nine test data sets were predicted correctly from the total 10 testing data sets (Fig. 11) with 90% success. The predictive ability of 90% is considered high, and only one silt type was predicted incorrectly. It is possible that heterogeneous and/or anisotropic conditions existed at this depth between the two wells and resulted in the wrong prediction of the silt zone. Another possible reason could be due to some factors that were not considered in this study such as lacking the SP log information. lithology if-then rules with its specific rule weighting, was established in this study for the Shui-Lin area. After the training work of the fuzzy lithology system was completed, the performance of training and the ability of prediction were validated Performance validation of fuzzy lithology system training (training results) The performance validation was employed to check the system s training performance by placing all or part 6. Discussion The original well survey of the SL-monitoring well included the GR log, the short (spacing) normal (16") resistivity and long (spacing) normal (64 ) resistivity curves. Because mud recycling was not adopted in drilling, and the plastic casing was installed quickly to avoid well collapse in some depth intervals, the logging data quality was of poor quality to identify lithology. The vicinity well, SL-2, recycled the mud (GELMUD consisting of brackish water and bentonite) during

10 272 B.Z. Hsieh et al. / Computers & Geosciences 31 (2005) Table 5 Fuzzy if-then lithology rules after fuzzy system training Rule 1 If GR is VL and DR is VH and Dt is (N/A) * Then Lithology is CS (1) ** Rule 2 If GR is L and DR is H and Dt is (N/A) * Then Lithology is MS (1) Rule 3 If GR is (N/A) * and DR is H and Dt is M Then Lithology is MS (0.8) Rule 4 If GR is M and DR is M and Dt is M Then Lithology is FS (1) Rule 5 If GR is M and DR is M and Dt is L Then Lithology is FS (1) Rule 6 If GR is (N/A) * and DR is H and Dt is H Then Lithology is FS (0.8) Rule 7 If GR is H and DR is L and Dt is H Then Lithology is Z (0.6) Rule 8 If GR is H and DR is M and Dt is H Then Lithology is Z (0.4) Rule 9 If GR is H and DR is M and Dt is M Then Lithology is Z (0.4) Rule 10 If GR is VH and DR is L and Dt is H Then Lithology is C (0.4) Rule 11 If GR is VH and DR is VL and Dt is H Then Lithology is C (1) Rule 12 If GR is VH and DR is VL and Dt is VH Then Lithology is C (1) Abbreviation identify: VL (very Low) ; L (low) ; M (medium) ; H (high) ; VH (very high) CS (coarse sand); MS(medium sand); FS(fine sand); Z(silt); C(clay). (N/A) * : Rule did not use this component after system training (a reduced rule works here). ** The rule weighting value. Fig. 10. Comparison between true lithology and fuzzy lithology in training period. drilling, and the well was logged by Schlumberger Corporation. The log quality was sufficient to identify lithology. It should be noted that the mudcake resistivity (Rmc) and mudfiltrate resistivity (Rmf), both with values of about 4 O-m as determined from the log header, indicate that the drilling mud in the SL-2 well was just salty enough to act as a conductive fluid for the SP to operate and to yield sufficient contrast between the invaded and uninvaded zones, thereby allowing the Induction Phasor log to operate. Results from the fuzzy lithology system for the SL-2 well were then correlated with the core analysis lithologies from the SL-monitoring well in this study. In the performance validation of the system training, 36 training data sets were identified correctly from the total 40 training data sets. The training performance was

11 B.Z. Hsieh et al. / Computers & Geosciences 31 (2005) Fig. 11. Comparison between true lithology and fuzzy lithology in testing period. 90%. In the results of the system prediction ability validation, nine test data sets were predicted successfully from the total 10 test data sets. The predictive ability was 90%, and it is considered high compared to Cuddy s (2000) and Fung et al. s (1997) studies. Another way to check the prediction accuracy for both training and testing is based on the coefficient of correlation (Fung et al., 1997). A high value of the coefficient of correlation means the system results have high correlations to the original core data. In this study, the calculated training correlation was 0.925, and the calculated testing correlation was also high (up to 0.928). In the (Fung et al. s (1997) study, the best training correlation was 0.917, and the best testing correlation was Compared with their results (even though they had a different output variable to be porosity ) we can conclude that the prediction accuracy of our fuzzy lithology system is acceptable. The lithologic results from core analysis, well logging and fuzzy lithology are compared in Fig. 12, in which the three major columns represent lithologies from the three methods. The groundwater formations between 100 and 198 m (drill depths) in the SL-2 well were divided into either sands or shales based on conventional well logging analysis of the log curve shapes and two basic rules: (Rule 1) IF the GR reading is low, IF the separation of deep and shallow resistivity curves (DR) is wide, and IF the interval transit time (Dt) is short, THEN the lithology of the formation is sand. (Rule 2) IF the gamma-ray GR is high, IF the separation of deep and shallow resistivity curves (DR) is narrow, and IF the interval transit time (Dt) is long, THEN the lithology of the formation is shale. The words used in the above sentences, low and high, mean the relative degree of GR reading. Usually, maximum values of GR readings are used to infer a shale base line, and minimum values will be used to set up a sand base line. The word low means close to the sand base line, and the word high means close to the shale base line. The words wide and narrow refer to the relative degree of separation between the deep and shallow resistivity curves. The word wide means the value is close to the maximum separation for the given depth interval, and the word narrow is just the opposite. Also, the words short and long refer to the relative values of the interval transit times measured in BHC log. The well logging method can easily delineate a permeable sand formation from log characteristics (Fig. 12), but identification of silts and determination of sands with varying grain sizes (from coarse to fine)

12 274 B.Z. Hsieh et al. / Computers & Geosciences 31 (2005) Fig. 12. Lithology results: comparison of core analysis, well logging, and fuzzy system. are more subjective and difficult. This shortcoming can be improved by our fuzzy lithology system analysis. This study s lithology system included C, Z, FS, MS, and CS, all of which are common in Shui-Lin area. Because gravels are not found in the depth range from 100 to 198 m in this area, they were omitted. On the other hand, this fuzzy lithology system cannot recognize a gravel lithology because the system did not include any experience while system training. In this case, the fuzzy lithology system is not appropriate for gravel formations

13 B.Z. Hsieh et al. / Computers & Geosciences 31 (2005) (like those close to the upper section of the Choushui River alluvial fan). Furthermore, this study involves a clastic aquifer rather than a carbonate aquifer; however, some studies have developed similar method can be applied to carbonate reservoirs (Chang et al., 1997; Cuddy, 2000). This might be of interest to middle- Eastern oil field analysts. groundwater monitoring network set up by Water Resources Agency, Ministry of Economic Affairs, Taiwan. We also give special thanks to John Doveton and an anonymous reviewer for their valuable review comments that made our study more integrated. 7. Conclusions A fuzzy lithology system based on well logs from the Shui-Lin area of Taiwan was constructed for identifying formation lithology with varying grain sizes of a groundwater aquifer in this study. The specific fuzzy sets of input variables were established, and a fuzzy lithology rule-based database containing 12 fuzzy lithology if-then rules with its specific rule-weighting was formulated for the Shui-Lin area. The conclusions are: (1) The prediction accuracy of fuzzy lithology system was fairly good ( 90% for predictive ability and 90% or better for the coefficient of correlation) based on the results of the testing performance, and the calculated coefficient of correlation of training and testing. (2) The compared lithologic results by core analysis, well logging and fuzzy lithology show that the conventional well logging method can easily distinguish a permeable sand formation from log characteristics, but identification of silts and determination of sands with varying grain sizes are more subjective and difficult. As illustrated in this research, our fuzzy lithology system can improve the definition of grain size. Although there is some subjectivity in the fuzzy lithology system, it enables the log analyst to make a more objective final decision than by conventional well log analysis. (3) This methodology can be particularly useful for large aquifers involving multi wells where only a few core analyses are available. Acknowledgments The authors thank Chinese Petroleum Corporation of Taiwan for supplying logs from the SL-2 well. We appreciate the core analyses furnished by Central Geological Survey of Taiwan, and the groundwater aquifer information in the Shui-Lin area from the References Asquith, G., Gibson, C., Basic Well Log Analysis for Geologists. AAPG Publications, Tulsa, OK 216pp. Chang, H.C., Chen, H.C., Fang, J.H., Lithology determination from well logs with fuzzy association memory neural network. IEEE Transactions on Geoscience and Remote Sensing 35 (3), Chapellier, D., Well Logging in Hydrogeology. A.A. Balkema Publishers, Brookfield, MA 175pp. Cuddy, S.J., Litho-facies and permeability prediction from electrical logs using fuzzy logic. SPE Reservoir Evaluation & Engineering 3 (4), Dewan, J.T., Essentials of Modern Open-Hole Log Interpretation. PennWell Publishing Company, Tulsa, OK 361pp. Fung, C.C., Wong, K.W., Wong, P.M., A self-generating fuzzy rules inference for petrophysical properties prediction. In: Proceedings of the IEEE International Conference on Intelligent Processing System. Beijing, China, pp Hsieh, B.Z., Estimation of aquifer s formation strength from well logging data. M.Sc. Thesis, National Cheng Kung University, Tainan, Taiwan, 134 pp (In Chinese). Huang, Y., Gedeon, T.D., Wong, P.M., A practice fuzzy interpolator for prediction of reservoir permeability. In: Proceedings of the IEEE International Conference on Fuzzy System. Seoul, South Korea, pp. III-1528 III Klir, G., Yuan, B., Fuzzy Sets and Fuzzy Logic, Theory and Applications. Prentice-Hall, Englewood Cliffs, NJ 574pp. Lin, Z.S., Hsieh, B.Z., Cai, M.Y., Tang, Y.D., Lee, C.C., Chen, S.T., The Hydro-geologic characteristics estimation of subsidence area in Yun-Lin, Taiwan. In: Proceedings of the 2nd Meeting of the Groundwater Resources and Water Quality Protection. Tainan, Taiwan, pp (In Chinese). MATLAB, Fuzzy Logic Toolbox User s Guide. The MathWorks, Inc., Natick, MA 217pp. Sheriff, R.E., Geldart, L.P., Exploration Seismology. Cambridge University Press, Melbourne, Australia 592pp. Temples, T.J., Waddell, M.G., Application of petroleum geophysical well logging and sampling techniques for evaluating aquifer characteristics. Ground Water 34 (3), Yen, J., Langari, R., Fuzzy Logic Intelligence. Control and Information. Prentice-Hall, Englewood Cliffs, NJ 548pp.