188bet 88betapp Application of machine learning techniques in estimation of fracture porosity using fuzzy inference system for a FGB reservoir in

Summary

Determination of porosity of a fractured granite basement (FGB) reservoir in 188bet 88betapp Cuu Long basin has always been a challenge for petrophysicists. In this study, an analysis of fracture porosity was successfully conducted, using a machine-learning technique, i.e., fuzzy inference system (FIS), thewell log data including gammaray(GR), deep resistivity (LLD), shallow resistivity (LLS), sonic (DT), bulk density (RHOB), neutron porosity (NPHI), photoelectric factor (PEF) and caliper (CAL) from two wells BHX01 and BHX02, were used as 188bet 88betapp input for FIS analyses. Fracture porosity calculated by conventional method was found between 0.01 and 2.24% for BHX01 and between 0.15 and 6.63% for BHX02, respectively. These values match very well with those predicted by various FIS techniques, i.e. Sugeno, Mamdani and Subtractive FIS models. It is expected that 188bet 88betapp approach of using FIS in petrophysical analysis as presented in this paper can be further applied for other fractured granite basement reservoirs in 188bet 88betapp Cuu Long and Nam Con Son basins, offshore southern Vietnam.

Key words: Machine learning, fuzzy interference system (FIS), well log analysis, fracture porosity, Cuu long basin.

1. Introduction

As shown in Figure 1 188bet 88betapp study site is located in 188bet 88betapp northern Cuu Long basin, which was formed by 188bet 88betapp fragmentation, rifting, and subsidence of Pre-Tertiary basement and later filled with 188bet 88betapp-end-of-Eocene to Pliocene-Quaternary continental, shallow marine and coastal plain deposits.

Common methods used to estimate primary porosity of a clastic reservoir are not always suitable to estimate 188bet 88betapp fracture porosity. As a result, petrophysicists keep trying to find new approaches to estimate fracture porosity. In this study, porosity of a fractured granite basement reservoir will be estimated by using a soft computing technique known as fuzzy inference system (FIS), whose results will be compared with those calculated based on a conventional method [1].

Concept of soft computing was first put forward by Zadeh [2], which is known to include 188bet 88betapp major methods such as fuzzy logic, evolutionary computation, neural computing, and probabilistic reasoning.

 Fuzzy interference systems (FIS) are designed using fuzzy set, which is a kind of mathematical set, where each element of 188bet 88betapp set has a degree of membership. A fuzzy set does not require a crisp and a clearly defined boundary. It can contain elements with a partial degree of membership. A crisp set of reservoir porosity may include{fair, very good} where 188bet 88betapp degree of membership of an element (denoted as µ) is either 0 or 1; thus, there can only be one kind of reservoir porosity. For example, in Figure2a, if porosity (φf) is greater than 0.5, reservoir porosity is very good (µ = 1.0), but if porosity is lower than 0.5, it is poor (µ = 0). A Fuzzy set, on 188bet 88betapp other hand, allows each element to have partial membership; thus, one can write a fuzzy set as {poor, fair, good, very good}. As an example, in Figure 2b, if porosity is 0.4, it is classified as fair.

Figure 1. Study location.

Fuzzy inference (reasoning) is 188bet 88betapp actual process of mapping from a given input to an output using fuzzy logic. Figure 3 shows 188bet 88betapp architecture of a fuzzy inference system.

As seen in Figure 3 188bet 88betapp fuzzifier converts 188bet 88betapp raw input data into a linguistic variable using 188bet 88betapp membership function stored in 188bet 88betapp fuzzy knowledge base. 188bet 88betapp inference engine further converts 188bet 88betapp fuzzy input to 188bet 88betapp fuzzy output using if-then type fuzzy rules. 188bet 88betapp defuzzifier converts 188bet 88betapp fuzzy output of 188bet 88betapp inference engine to crisp using membership functions analogous to 188bet 88betapp ones used by 188bet 88betapp fuzzifier.

There are two main types of fuzzy interference methods based on clustering of numerical data, i.e. C-means and Subtractive. 188bet 88betapp former is a supervised algorithm that can only be used when there is a set of inputs and corresponding outputs to those inputs (training set). 188bet 88betapp final output of fuzzy C-means is not a FIS but rather a list of cluster centres and several membership grades for each data point. One can use 188bet 88betapp information returned by 188bet 88betapp fuzzy C-means routine to build a FIS. Two types of FIS can be modelled using C-means clustering, i.e. Mamdani and Sugeno that are similar in many aspects, and namely, 188bet 88betapp first two parts of 188bet 88betapp fuzzy inference process, fuzzifying 188bet 88betapp inputs and applying 188bet 88betapp fuzzy operator in 188bet 88betapp inference engine (Figure 3) are exactly 188bet 88betapp same. 188bet 88betapp most fundamental difference between Mamdani type FIS and Sugeno type FIS is 188bet 88betapp way 188bet 88betapp crisp output is generated from 188bet 88betapp fuzzy inputs. While Mamdani FIS uses 188bet 88betapp technique of defuzzification of a fuzzy output, Sugeno FIS uses weighted average to compute 188bet 88betapp crisp [3]. So basically, Sugeno model bi-passes 188bet 88betapp defuzzification. As a result, in Mamdani model there is an output membership function whereas in Sugeno model there is no output membership function. Subtractive is an unsupervised algorithm. It can be utilised when there are no corresponding outputs for a set of input data. This method is focusing on finding regions in 188bet 88betapp feature space with high densities of data points. 188bet 88betapp data points within a prespecified, fuzzy radius are then subtracted (removed), and 188bet 88betapp algorithm proceeds its search for a new point with 188bet 88betapp highest number of neighbours. 188bet 88betapp iteration continues until all points have been tested. 188bet 88betapp quality of 188bet 88betapp solution depends strongly on 188bet 88betapp choice of initial values [4].

Figure 2. Membership function: (a) crisp set; (b) fuzzy set.

Figure 3. Architecture of a fuzzy inference system.

Application of fuzzy interference systems in petrophysics has been used over 188bet 88betapp past two decades. Fang and Chen [5] predicted porosity and permeability from 188bet 88betapp compositional and textural characteristics of sandstones, using fuzzy modelling which is not only assumption-free but also tolerant of outliers. Fuzzy modelling is capable of making both linguistic and numeric predictions based on qualitative knowledge and/or quantitative data. Martinez et al. [6] presented a technique for 188bet 88betapp identification and characterisation of naturally fractured reservoirs. A fuzzy inference system was implemented in their study to obtain a fracture index using only data from conventional well logs. Additionally, model from O’Connell and Budiansky [7] for 188bet 88betapp prediction of elastic properties of fractured porous rocks is inverted using genetic algorithms to obtain crack density and crack aspect ratio. 188bet 88betapp results obtained are compared with core information available. Hambalek and Gonzalez [8] applied fuzzy logic theory in order to establish a narrow relation between well logs and 188bet 88betapp seven rock types (lithofacies) of 188bet 88betapp sedimentological model that describes a very complex reservoir in eastern Venezuela. Core analysis of five wells and 188bet 88betapp established fuzzy relations are used to get 188bet 88betapp lithofacies description and possible values of permeability in eighteen wells of 188bet 88betapp same area having only electrical logs. 188bet 88betapp efficiency of 188bet 88betapp algorithm developed was verified against a control well with both log and core data. 188bet 88betapp results are very satisfactory and open 188bet 88betapp possibilities for future research and application. Abdulraheem [9] presented 188bet 88betapp use of fuzzy logic modelling to estimate permeability from wireline logs data for a carbonate reservoir in 188bet 88betapp Middle East. In this study, correlation coefficients are used as criteria for checking whether a given wireline log is suitable as an input for fuzzy modelling.

2. Methodology

Well log data gamma ray (GR), deep resistivity (LLD), shallow resistivity (LLS), sonic (DT), bulk density (RHOB), neutron porosity (NPHI), photoelectric factor (PEF), and caliper (CAL) were collected from 2 wells BHX01 and BHX02 at a study site in Cuu Long basin, Vietnam.

In this research, 188bet 88betapp depth interval from 2,515m to 3,015m of well BXH01 and that from 3,050m to 3,870m of well BHX02 were selected. Four reservoir zones of well BHX01 and five reservoir zones of well BHX02 [10] were used in 188bet 88betapp analyses as shown in Table 1.

188bet 88betapp flowchart of 188bet 88betapp study is shown in Figure 4. First of all, fractureporositieswerecalculatedusingaconventional method suggested by Elkewidy & Tiab [1] that is also described in detail in Giao and Sandunil [11] by Equations 1 - 3. Matrix density will be assumed to be 2.71g/cc, which is for limestone, and fluid density is 1.00g/cc, which is for water. This is because parameters of wireline logging tools used to acquire formation density and neutron porosity of formation are calibra and 188bet 88betapp remaining 25% of 188bet 88betapp well log data are used for prediction. In 188bet 88betapp second analysis (Analysis II), 188bet 88betapp well log data of zones 3 and 4 of BXH01 were used to In 188bet 88betapp next step, two analyses were conducted to predict porosity using three different FIS models, i.e., Sugeno, Mamdani and Subtractive. In 188bet 88betapp first analysis (Analysis I), FIS-based prediction was done for every reservoir zone of wells BHX01 and BHX02, separately, i.e., for each zone 75% of well log data are used for training train 188bet 88betapp FIS models to predict 188bet 88betapp fracture porosity of zones 1 and 2 of BHX02 as indicated in Table 1. 

Where:

φt: Total porosity, fraction;

φD: Porosity calculated from bulk density, fraction;

φN: Neutron porosity, fraction; φf: Fracture porosity, fraction; ρb: Bulk density, g/cc;

ρma: Matrix density, g/cc; ρf: Fluid density, g/cc;

m: Cementation factor, dimensionless.
  

Figure 4. Flow chart of 188bet 88betapp methodology.

Table 1. Measured depth and true vertical depth of 188bet 88betapp analysed reservoir zones

Table 2. Fracture porosity calculated by conventional approach [1]

Table 3. Results of fracture porosity predicted by FIS in Analyses I and II

Table 4. Correlation coefficients in two Analyses I & II, using Sugeno, Mamdani and Subtractive models

Figure 5. Fracture porosity calculated for zones 1 - 4, well BHX01, Analysis I by (a) Sugeno model, (b) Mamdani model, (c) Subtractive model.

Figure 6. Fracture porosity calculated for zones 1 - 5, well BHX02, Analysis I by (a) Sugeno model, (b) Mamdani model, (c) Subtractive model.

Figure 7. Fracture porosity calculated by Sugeno, Mamdani and Subtractive models for zones 1 and 2, well BHX02, Analysis II.

 3. Results and discussion

188bet 88betapp average fracture porosities for each reservoir zone as calculated using Elkewidy & Tiab’s method [1] shown in Table 2 are found to be between 0.03 and 2.24 for BHX01, and 0.18 and 5.43 for BHX02, respectively. These conventionally-calculated values were further used to train 188bet 88betapp FIS models. Table 3 shows 188bet 88betapp results of Analysis I, indicating 188bet 88betapp average fracture porosities predicted by Sugeno, Mamdani and Subtractive in comparison with those calculated by 188bet 88betapp conventional method.

188bet 88betapp results of fracture porosity predicted by FIS models are plotted in Figure 5 and Figure 6 as well as shown in Table 3, which are quite close to those calculated by 188bet 88betapp conventional method shown in Table 2. Among three FIS models, 188bet 88betapp values predicted by two models of Sugeno and Subtractive are better than those obtained by Mamdani model. This remark is further supported by 188bet 88betapp calculated correlation coefficient of each FIS analysis as shown in Table 4, which are lower in case of Mamdani model. Out of 188bet 88betapp three models, Subtractive model gave 188bet 88betapp best results.

As seen in Figures 5 - 7, 188bet 88betapp fracture porosity curves predicted by Sugeno and Subtractive models follow well 188bet 88betapp shape of 188bet 88betapp conventionally-calculated curve of φf.

4. Conclusions

188bet 88betapp FIS Sugeno and Subtractive models proved to be good methods to predict fracture porosity, which is between 0.00 - 2.31 and 0.01 - 2.27 for well BHX01, 0.10 - and 0.16 - 6.58 for well BHX02, respectively.

Fracture porosity predicted by FIS Mamdani are more deviated from 188bet 88betapp values calculated by Elkewidy & Tiab’s method [1] comparing to those predicted by  Sugeno and Subtractive models, 188bet 88betapp fact which is additionally supported by lower values of correlation coefficient.

Out of 188bet 88betapp three models employed, FIS Subtractive was 188bet 88betapp best to predict fracture porosity with 188bet 88betapp highest correlation coefficients.

Although Analysis I that used 188bet 88betapp well log data in one well to predict fracture porosity prediction for 188bet 88betapp same well gave better results than Analysis II that used 188bet 88betapp well data from one well to predict fracture porosity in another well, 188bet 88betapp results obtained by 188bet 88betapp latter are also very satisfactory and encouraging for a wider application in practice to predict 188bet 88betapp porosity of a fractured granite basement reservoirs in 188bet 88betapp Cuu Long and Nam Con Son basins.

References

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3. Abdelwahab Hamam, Nicolas D.Georganas. A comparisonof Mamdaniand Sugenofuzzyinferencesystems for evaluating 188bet 88betapp quality of experience of Hapto-Audio- Visual applications. 2008 IEEE International Workshop on Haptic Audio Visual Environments and Games. 18 - 19 October, 2008: p. 87 - 92.

4. Muriel Bowie. Fuzzy clustering, feature selection, and membership function optimization. Seminar Paper, Department of Informatics, University of Fribourg, Switzerland. 2004.

5. J.H.Fang, H.C.Chen. Fuzzy  modeling  and  188bet 88betapp prediction of porosity and permeability from 188bet 88betapp compositional and textural attributes of sandstone. Journal of Petroleum Geology. 1997; 20(2): p. 185 - 204.

6. L.P.Martinez, R.G.Hughes, M.L.Wiggins. Identification and characterization of naturally fractured reservoir using conventional well logs. University of Oklahoma. 2002.

7. Richard J.O'Connell, Bernard Budiansky. Seismic velocities in dry and saturated cracked solids. Journal of Geophysical Research. 1974; 79(35): p. 5412 - 5426.

8. Nancy Hambalek, Reinaldo Gonzalez. Fuzzy logic applied to lithofacies and permeability forecasting. SPE 81078. SPE Latin America and Caribbean Petroleum Conference, Trinidad. 27 - 30 April, 2003.

9. Abdulazeez Abdulraheem, Emad Sabakhy, Mujahed Ahmed, Aurifullah Vantala, Putu D. Raharja, Gabor Korvin. Estimation of permeability from wireline logs in a Middle East carbonate reservoir using fuzzy logic. SPE 105350. SPE Middle East Oil and Gas Show and Conference, Manama, Bahrain. 11 - 14 March, 2007.

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