đăng nhập 188bet 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 đăng nhập 188bet 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 đăng nhập 188bet 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 đăng nhập 188bet approach of using FIS in petrophysical analysis as presented in this paper can be further applied for other fractured granite basement reservoirs in đăng nhập 188bet 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 đăng nhập 188bet study site is located in đăng nhập 188bet northern Cuu Long basin, which was formed by đăng nhập 188bet fragmentation, rifting, and subsidence of Pre-Tertiary basement and later filled with đăng nhập 188bet-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 đăng nhập 188bet 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 đăng nhập 188bet 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 đăng nhập 188bet 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 đăng nhập 188bet 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 đăng nhập 188bet 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 đăng nhập 188bet actual process of mapping from a given input to an output using fuzzy logic. Figure 3 shows đăng nhập 188bet architecture of a fuzzy inference system.

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

There are two main types of fuzzy interference methods based on clustering of numerical data, i.e. C-means and Subtractive. đăng nhập 188bet 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). đăng nhập 188bet 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 đăng nhập 188bet information returned by đăng nhập 188bet 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, đăng nhập 188bet first two parts of đăng nhập 188bet fuzzy inference process, fuzzifying đăng nhập 188bet inputs and applying đăng nhập 188bet fuzzy operator in đăng nhập 188bet inference engine (Figure 3) are exactly đăng nhập 188bet same. đăng nhập 188bet most fundamental difference between Mamdani type FIS and Sugeno type FIS is đăng nhập 188bet way đăng nhập 188bet crisp output is generated from đăng nhập 188bet fuzzy inputs. While Mamdani FIS uses đăng nhập 188bet technique of defuzzification of a fuzzy output, Sugeno FIS uses weighted average to compute đăng nhập 188bet crisp [3]. So basically, Sugeno model bi-passes đăng nhập 188bet 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 đăng nhập 188bet feature space with high densities of data points. đăng nhập 188bet data points within a prespecified, fuzzy radius are then subtracted (removed), and đăng nhập 188bet algorithm proceeds its search for a new point with đăng nhập 188bet highest number of neighbours. đăng nhập 188bet iteration continues until all points have been tested. đăng nhập 188bet quality of đăng nhập 188bet solution depends strongly on đăng nhập 188bet 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 đăng nhập 188bet past two decades. Fang and Chen [5] predicted porosity and permeability from đăng nhập 188bet 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 đăng nhập 188bet 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 đăng nhập 188bet prediction of elastic properties of fractured porous rocks is inverted using genetic algorithms to obtain crack density and crack aspect ratio. đăng nhập 188bet 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 đăng nhập 188bet seven rock types (lithofacies) of đăng nhập 188bet sedimentological model that describes a very complex reservoir in eastern Venezuela. Core analysis of five wells and đăng nhập 188bet established fuzzy relations are used to get đăng nhập 188bet lithofacies description and possible values of permeability in eighteen wells of đăng nhập 188bet same area having only electrical logs. đăng nhập 188bet efficiency of đăng nhập 188bet algorithm developed was verified against a control well with both log and core data. đăng nhập 188bet results are very satisfactory and open đăng nhập 188bet possibilities for future research and application. Abdulraheem [9] presented đăng nhập 188bet use of fuzzy logic modelling to estimate permeability from wireline logs data for a carbonate reservoir in đăng nhập 188bet 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, đăng nhập 188bet 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 đăng nhập 188bet analyses as shown in Table 1.

đăng nhập 188bet flowchart of đăng nhập 188bet 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 đăng nhập 188bet remaining 25% of đăng nhập 188bet well log data are used for prediction. In đăng nhập 188bet second analysis (Analysis II), đăng nhập 188bet well log data of zones 3 and 4 of BXH01 were used to In đăng nhập 188bet next step, two analyses were conducted to predict porosity using three different FIS models, i.e., Sugeno, Mamdani and Subtractive. In đăng nhập 188bet 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 đăng nhập 188bet FIS models to predict đăng nhập 188bet 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 đăng nhập 188bet methodology.

Table 1. Measured depth and true vertical depth of đăng nhập 188bet 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

đăng nhập 188bet 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 đăng nhập 188bet FIS models. Table 3 shows đăng nhập 188bet results of Analysis I, indicating đăng nhập 188bet average fracture porosities predicted by Sugeno, Mamdani and Subtractive in comparison with those calculated by đăng nhập 188bet conventional method.

đăng nhập 188bet 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 đăng nhập 188bet conventional method shown in Table 2. Among three FIS models, đăng nhập 188bet values predicted by two models of Sugeno and Subtractive are better than those obtained by Mamdani model. This remark is further supported by đăng nhập 188bet calculated correlation coefficient of each FIS analysis as shown in Table 4, which are lower in case of Mamdani model. Out of đăng nhập 188bet three models, Subtractive model gave đăng nhập 188bet best results.

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

4. Conclusions

đăng nhập 188bet 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 đăng nhập 188bet values calculated by Elkewidy & Tiab’s method [1] comparing to those predicted by  Sugeno and Subtractive models, đăng nhập 188bet fact which is additionally supported by lower values of correlation coefficient.

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

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

References

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2. Lotfi A. Zadeh. Fuzzy logic, neural network and soft computing. Communication of đăng nhập 188bet ACM. 1994; 37(3): p. 77- 84.

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5. J.H.Fang, H.C.Chen. Fuzzy  modeling  and  đăng nhập 188bet prediction of porosity and permeability from đăng nhập 188bet 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.

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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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